How do you simplify (a3b2)2

Answers

Answer 1

Answer:

a^6b^4

Step-by-step explanation:

(a³b²)²

a^6b^4

Answer 2

9514 1404 393

Answer:

  a⁶b⁴

Step-by-step explanation:

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

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These let us simplify the expression as follows:

  [tex](a^3b^2)^2=(a^3)^2(b^2)^2=a^{3\cdot2}b^{2\cdot2}=\boxed{a^6b^4}[/tex]

_____

Additional comment

It might be helpful to remember that an exponent signifies repeated multiplication.

  a·a·a = a³ . . . . . . 'a' is a factor 3 times, so the exponent is 3.

Similarly, ...

  (a³)² = (a³)·(a³) = (a·a·a)·(a·a·a) = a⁶


Related Questions

Given the triangle below, find the angle θ in radians. Round to four decimal places.

Answers

Answer:

θ = 0.9626

Step-by-step explanation:

Hi there!

We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:

[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]

Plug in the given information

[tex]\displaystyle cos\theta=\frac{4}{7}[/tex]

Use the inverse cosine ratio

[tex]\displaystyle \theta=cos^-^1(\frac{4}{7})[/tex]

Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)

[tex]\displaystyle \theta=0.9626[/tex]

Therefore, θ = 0.9626 when rounded to four decimal places.

I hope this helps!

Answer:

theta = 0.9626 radians

Step-by-step explanation:

cos theta = a/h

cos theta = 4/7 = 0.5714

so, the angle theta = arc cos 0.5714 =

55.1520 °

in radians => 55.1520 × π / 180°

= 0.9626 radians

Please Help Me Do This I cant understand it no matter how hard I try. (Problem in the image)

Answers

9514 1404 393

Answer:

  7.28

Step-by-step explanation:

Consider the attachment. There, we have identified a point C that makes ABC a right triangle with the right angle at C.

The Pythagorean theorem gives you the relationship between side lengths of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

  AB² = AC² +BC²

We can count grid squares to find the lengths of AC and BC. They are 2 units and 7 units, respectively. This means ...

  AB² = 2² +7²

  AB² = 2·2 +7·7 = 4 +49 = 53

When we know the square, we can find what it is the square of by taking the square root. Generally, a calculator is required for this.

  AB = √53 ≈ 7.2801099

When we round this number to two decimal places (the nearest hundredth), we get ...

  AB ≈ 7.28 . . . units

_____

Additional comments

You will notice that the length AC in the diagram is the difference of the x-coordinates of points A and B. Similarly, the length BC in the diagram is the difference of y-coordinates. Then the square AB² is the sum of the squares of these differences. The length AB is the square root of that sum.

In general, this is how you find the length of a line segment from its end point coordinates.

__

A little magic, perhaps: You may find that repeating the 11-digit number on the first line several times a day for a few days will help to moderate your difficulty understanding this. The numbers convey an energy that is intended to counteract the brain block that often arises when seeing a math problem.

Derrek wants to find another way to show 6 thousands. Which value is equal to 6 thousands?

Answers

Answer:

6,000

Step-by-step explanation:

60 hundreds.

600 tens.

The manager at a computer recycling plant says it takes workers a minimum of 120 seconds to break down a computer monitor. The exact amount of time depends on the number of screws in the computer that must be removed. It takes 10 seconds to remove each screw, and then an additional 30 seconds to sort the computer parts into their appropriate containers for recycling. Write an inequality that determines the minimum number of screws that are in each computer monitor.

Answers

Answer: 120 + 10s + 30

Step-by-step explanation:

120 + 10s + 30

let "s" be the amount of screws

During a science lab, four-fifths of the class completed the lab and earned a grade of 100. What percent of the class didnt earn a grade of 100?
F. 60%
G. 80%
H. 20%
J.45%

Answers

Answer: H. 20%

Step-by-step explanation: if 4/5 got 100 then 80% got 100 so the other 20% did not get a 100

Calculate the area of this section of floor in square feet.

Answers

Answer:

A total= 0.6703125 ft²

Step-by-step explanation:

A1= 3.9× 14.3= 55.77 in²

A2=1/2 × 14.3× ( 9.6-3.9)= 40.755 in²

A total= A1+ A2= 55.77+40.755=96.525 in²

1 ft= 12 in , 1ft²= 144 in²

Atotal= 96.525÷144= 0.6703125 ft²

x ^ 2 − 17x − 60

Which expression is equivalent to the expression above?

(Please explain in simple terms cause, it's usually hard for me to understand)

Answers

[tex] {x}^{2} - 17x - 60 \\ (x + 3)(x - 20)[/tex]

First we put parentheses and in each bracket we put (X) and then we put the signs x² is positive and the 17X before it is a negative q is positive with negative —> negative, and negative before 17X and negative before the 60 —> positive. And then the number that does not have (x) where did it come from, for example 60 came from 20 x 3 or 30 x 2...etc. We can verify this by multiplying the parentheses together and the same number comes out .

Or it can be checked by multiplying the first bracket 3 with x from the second parenthesis comes out 3X and negative 20 from the second parenthesis with X from the first parenthesis and subtract 3X from –20xcomes out –17X .

I hope I helped you^_^

I'm a little stuck on this, could I get some help? C:

How much would you need to deposit in an account each month in order to have $50,000 in the account in 10 years? Assume the account earns 5% annual interest compounded monthly.

Thank you, and I am eternally grateful.

Answers

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Answer:

  $321.99

Step-by-step explanation:

Use the annuity formula and solve for P.

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . value of a series of deposits P earning rate r compounded monthly for t years.

  50,000 = P(12/0.05)((1 +0.05/12)^(12·10) -1) = P(240)(0.64700950)

  P = 50,000/155.282279 = 321.99

You would need to deposit $321.99 in the account each month to have $50,000 in 10 years.

Twenty is 12% of what number? Round to two decimal places if needed.​

Answers

Answer:

166,67

Step-by-step explanation:

We want to find a number x which 12% is 20:

x * 0.12 = 20

x = 20 / 0.12

x = 166,67

Given log4(3) =0.7925 and log4(5) =1.1610, use log properties to find log4(300).

Answers

Answer:

4.1145

Step-by-step explanation:

You can use the following formula to solve this kind of problems,

[tex] log_{a}(b) + log_{a}(c) = log_{a}(bc) [/tex]

So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.

[tex] log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145[/tex]

the sum of 3 and a number

Answers

Answer:

the number will vary the answer

Step-by-step explanation:

3×1=3

3×2=6

Let f(x) = x - 3 and g(x) = x + 11 find f(x) times g(x)

What is the answer?

Answers

f(x) *g(x) = (x-3)(x+11) = x^2 +11x -3x -33 = x^2 +8x -33

Sorry if its wrong :(

2. What is the distance between points A and B?

A. -6 units
B. -1 unit
C. 5 units
D. 6 units

Answers

Answer:

5 units

Subtract -6 and -1, and you get -5. -5 can't be the answer since we are asked to find the distance, so it is the absolute value of -5, 5.

Answer:

D) 6 units

Explanation:

Point A is 5 units away from 0 (the middle)

Point B is 1 unit away from 0

5 + 1 = 6

Distance between two points cannot be negative

Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace.

Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number.


31%


8%


4%


25%

Answers

Answer:

8%

Step-by-step explanation:

Ok, there is 52 cards per deck, 13 per suit ( club, diamond, heart, and spade)

if you multiply 13 by 4 ( 4 is dependent on the number of suit, and 4 will always be the number of suit )

The probability is 8%.

Why, because 25 would be pulling a random card and your saying you want the suit to be diamond the probability of you getting a random diamond card would be 25%. But were not doing that. So cross out 31% and 25%.

Also, 4% would be as your counting 100 cards. So that leaves me with 8%.

The median speed at which Dave drove to work was __________. 63 miles per hour 62 miles per hour 58.89 miles per hour 59 miles per hour

Answers

Step-by-step explanation:

Dave run with was 63 miles

Evaluate the expression 4x + 6 -y^2 when x=-3 and y=4

Answers

4*(-3) + 6 -4^2=
-12+6-16=
-22
Answer (-22)

The expression 4x + 6 -y^2  when evaluated has a value of -22

How to evaluate the expression

From the question, we have the following parameters that can be used in our computation:

4x + 6 -y^2

Also, we have

x=-3 and y=4

Substitute the known values in the above equation, so, we have the following representation

4x + 6 -y^2 = 4 * -3 + 6 - 4^2

Evaluate

4x + 6 -y^2 = -22

Hence, the solution is -22

Read more about expression at

https://brainly.com/question/30492964

#SPJ6

Plzzz helppppp!!!!!!! 20+PTS and brainliest!!!!!!!!!!!!!!!
Please show work!!!!!!!!!!!

Answers

Refer to the equation y=mx+c

Find the value of x if

Answers

Answer:

C. 4

Step-by-step explanation:

We have the equation [tex]\sqrt[x]{81} =3[/tex] and are asked to find the value of x.

To find x, we need to find how many times 3 can go into 81 but as an exponent, instead of saying 3 * x it would be [tex]3^x[/tex].

So find the value of each exponent by replacing it with each answer choice :

[tex]3^8 = 6561[/tex]

[tex]3^{27} = 7.6255975e+12[/tex]

[tex]3^4 = 81[/tex]

[tex]3^2 = 9[/tex]

Since to the power of 4 equals the cube root in the original equation, therefore B. is the answer.

The graph of the reciprocal parent function, f(x) = ), is shifted 9 units
down and 11 units to the right to create the graph of g(x). What function is
g(x)?

Answers

Answer:

g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice

Step-by-step explanation:

I. If move right is +x and move down is -y

               then f(x) = [tex]\frac{1}{x}[/tex]

               +x = 11, -y = -9

                so g(x) = [tex]\frac{1}{x+11}-9[/tex]

Hope that help :D

5 times some number added to 8 amounts to 10 added to the product of 3 and the number

How do you solve this

Answers

9514 1404 393

Answer:

  the number is 1

Step-by-step explanation:

First of all, you need to know what you're solving. Here, we assume you're trying to find "the number."

__

Let n represent "some number." The given relation can be written using math symbols as ...

  5n +8 = 10 +3n

Subtract 3n +8 from both sides to separate the variable and the constant terms.

  2n = 2

  n = 1 . . . . . . . divide by 2

The number is 1.

__

Check

  5 times 1, added to 8 is 13. This amounts to the same thing as 10 added to the product of 3 and 1.

Write 7 hundred in standard form​

Answers

Answer:

700

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

7 hundred in standard form is 700.

Ruben is driving along a highway that passes through Barstow. His distance d, in miles, from Barstow is given by the equation
d = |210 − 60t|,
where t is the time, in hours, since the start of his trip and
0 ≤ t ≤ 5.
When will Ruben be exactly 90 miles from Barstow? (Enter your answers as a comma-separated list.)

Answers

The absolute value of a number returns the positive value of the given number. Ruben will be at exactly 90 miles in 2 hours or 5 hours

Given that:

[tex]d = |210 - 60t|[/tex]

To calculate t when [tex]d = 90[/tex], we have:

[tex]90 = |210 - 60t|[/tex]

Rewrite as:

[tex]|210 - 60t| = 90[/tex]

Remove absolute bracket

[tex]210 - 60t = 90 \ or\ 210 - 60t = -90[/tex]

Collect like terms

[tex]- 60t = -210 + 90 \ or\ - 60t = -210 -90[/tex]

[tex]- 60t = -120 \ or\ - 60t = -300[/tex]

Divide through by -60

[tex]t = 2 \ or\ t = 5[/tex]

Hence, Ruben will be at exactly 90 miles in 2 hours or 5 hours

Read more about absolute values at:

https://brainly.com/question/1301718

Help please! What is the length of the highlighted side? (Show work)

Answers

Answer:

7

Step-by-step explanation:

15ft - 8ft

Help I'll mark you as brainiest

Answers

Answer:

It is a function and 0to^2 shows your function dt.c and 4c-3 shows your function is wrong and the answer is 0 and 31/4 to the power of 25 and shows that the function is 8.

Step-by-step explanation:

what is the slope of a line containing 1,-2 and -1,5

Answers

Use the formula y2-y1/x2-x1

That gives you

5 - (-2) / -1 - 1 = -7/2

-7/2 should be your slope.

(Or it could be -3.5 in decimal form)

Sarah, Bob and Nellie are cousins. Sarah is half the age of Bob. In three years time Nellie will be twice as old as Sarah. Their ages at the moment add to 38 years. Determine the ages of Sarah, Bob and Nellie

Answers

9514 1404 393

Answer:

Sarah is 7Bob is 14Nellie is 17

Step-by-step explanation:

Let s, b, n represent the current ages of Sarah, Bob, and Nellie, respectively.

  s = b/2 . . . . . . Sarah is half Bob's age

  2(s+3) = n+3 . . . . in 3 years, Nellie will be twice Sarah's age

  s + b + n = 38 . . . . . their ages now add to 38

__

We can rearrange the first two equations to find Bob and Nellie's age in terms of Sarah's. Then we can substitute into the third equation to find Sarah's age.

  b = 2s . . . . . . multiply the first equation by 2

  2s +3 = n . . . . subtract 3 from the second equation and simplify

  s +(2s) +(2s+3) = 38 . . . . substitute for b and n

  5s = 35 . . . . . . . . . . . . subtract 3, collect terms

  s = 7 . . . . . . . . . . . . divide by 5

  b = 2(7) = 14

  n = 2(7) +3 = 17

Sarah is 7, Bob is 14, and Nellie is 17.

Someone please help me with 13 and 14 I’m really struggling

Answers

Answer:

Step-by-step explanation:

A CD with a diameter of 120 millimeters rotates a rate of 45 revolutions per minute. Find the linear speed of the CD in millimeters per minute. And find the angular speed of the CD in radians per minute

Answers

9514 1404 393

Answer:

16,965 mm/min90π ≈ 282.7 radians/min

Step-by-step explanation:

The circumference of the CD is ...

  C = πd

  C = π(120 mm) ≈ 376.99 mm

This is the distance a point on the edge of the CD will travel when making one revolution. It will travel 45 times this far when making 45 revolutions:

  (376.99 mm/rev)(45 rev/min) ≈ 16,965 mm/min

__

There are 2π radians in each revolution, so the angular speed is ...

  (2π rad/rev)(45 rev/min) = 90π rad/min ≈ 282.7 rad/min

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month.
Select one:
A. 18.147387
B. 2.846161
C. 0.332381
D. 0.052129

Answers

Answer:

D

Step-by-step explanation:

hhgxhsbjxkxjebdibfhejx

Which describes the relationship between the distance and the difference?\

Answers

Answer:

The distance is always the opposite of the difference.The distance is the absolute value of the difference.

Hope it helps you.Have a nice day!!

Answer:

The distance is the absolute value of the difference

Step-by-step explanation:

Sum is the when 2 or more numbers are added . Difference is the quantity at which 2 numbers differ i.e difference between 9 and 7 is 2. If you are talking about distance in reference to segment the distance ishow far apart two points are.

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In a mathematics class, half of the students scored 40 on an achievement test. With the exception of a few students who scored 80, the remaining students scored 58. Which of the following statements is true about the distribution of scores?A. The mean is greater than the median.B. The mean and the median are the same.C. The mean is less than the median.D. The mean is less than the mode. Commandancy of the The AlamoBejar, Feby. 24th. 1836To the People of Texas & All Americans in the WorldFellow Citizens & compatriotsI am besieged, by a thousand or more of the Mexicans under Santa Anna - I have sustained a continual Bombardment & cannonade for 24 hours & have not lost a man The enemy has demanded a surrender at - discretion, otherwise, the garrison are to be put to the sword, if the fort is taken I have answered the demand with a cannon shot, & our flag still waves proudly from the walls - I shall never surrender or retreat. Then, I call on you in the name of Liberty, of patriotism & everything dear to the American character, to come to our aid, with all dispatch - The enemy is receiving reinforcements daily & will no doubt increase to three or four thousand in four or five days. If this call is neglected, I am determined to sustain myself as long as possible & die like a soldier who never forgets what is due to his own honor & that of his countryVictory or Death.William Barrett Travis.Lt. Col. comdt.P. S. The Lord is on our side- When the enemy appeared in sight we had not three bushels of corn - We have since found in deserted houses 80 or 90 bushels and got into the walls 20 or 30 head of Beaves.APPARTSAUTHORWho created the source? What do you know about the author? What is the author's point of view?PLACE AND TIMEWhere and when was the source produced? 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