Answers
[tex]\boxed{\sf a^m\times a^n=a^{m+n}}[/tex]
[tex]\boxed{\sf a^m\div a^n=a^{m-n}}[/tex]
[tex]\\ \sf\longmapsto 3^{-6}\times( 3^4\div 3^0)^2[/tex]
[tex]\\ \sf\longmapsto 3^{-6}\times (3^{4-0})^2[/tex]
[tex]\\ \sf\longmapsto 3^{-6}\times 3^{4(2)}[/tex]
[tex]\\ \sf\longmapsto 3^{-6}\times 3^8[/tex]
[tex]\\ \sf\longmapsto 3^{-6+8}[/tex]
[tex]\\ \sf\longmapsto 3^2[/tex]
Answer:
[tex] {3}^{2} [/tex]
Step-by-step explanation:
[tex] {3}^{ - 6} \times ( {3}^{4} \div {3}^{0} {)}^{2} [/tex]
[tex] {3}^{4} \div {3}^{0} = {3}^{4 + 0} = {3}^{4} [/tex]
[tex] {3}^{ - 6} \times ( {3}^{4} {)}^{2} [/tex]
[tex]( {3}^{4} {)}^{2} = {3}^{4 \times 2} = {3}^{8} [/tex]
[tex] {3}^{ - 6} \times {3}^{8} = {3}^{ - 6 + 8} = {3}^{2} [/tex]
[tex] \boxed{\green{= {3}^{2} }}[/tex]
Related Questions
How would the expression (x^2 + 1)(y^2 + 4) be rewritten using Two Squares?
O A. (xy– 2)^2 - (4x+y)^2
B. ( xy- 2)^2 +(2x+y)^2
C. (xy+2)^2 +(x+2y)^2
D. (xy-2)^2+(x+2y)^2
Answers
The expression [tex](x^2 + 1)(y^2 + 4)[/tex] can be rewritten using Two Squares as [tex](xy-2)^2+(x+2y)^2[/tex]. The correct option is D.
What is Two Squares?The Two Squares identity is a special case of the identity: [tex](a^2 + b^2) = (a + b)^2 - 2ab[/tex].
This identity can be used to factorize certain expressions involving squares of variables.
By using the Two Squares identity, we can rewrite expressions in the form of a sum of two squares as a difference of squares, or vice versa. This can be useful in simplifying and solving equations in algebra.
We can use the Two Squares identity, which states that:
[tex](a^2 + b^2)(c^2 + d^2) = (ac - bd)^2 + (ad + bc)^2[/tex]
Comparing with the given expression, we can see that a = x, b = 1, c = y, and d = 2. Substituting these values into the Two Squares identity, we get:
[tex](x^2 + 1)(y^2 + 4) = (xy - 2)^2 + (x + 2y)^2[/tex]
Therefore, the answer is (D) [tex](xy-2)^2 + (x+2y)^2.[/tex]
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What is the correct order of steps for copying angle ABC?
A. Create point H at the intersection of the arcs created from point D, and draw a ray from point D through point H.
B. Draw a ray with the endpoint D, and place the compass on point B.
c. Keeping the compass at the same width, place it on point D, and swing an arc that creates point G.
D. Keeping the compass at the same width, place it on point G, and swing an arc that intersects the arc created from point D.
E. Open the compass to the distance between points E and F
F. Swing an arc that intersects rays BA and BC that creates point E on BA and F on BC.
1) AFCEDB
2) BFCEDA
3) AFCBDE
4) BFDECA
Answers
Answer: BFCEDA i took the test and got it right
Step-by-step explanation:
The correct order of steps for copying the angle ABC is BFCEDA.
What is copying the angle?The process of copying an angle through construction involves ensuring that the distance between the two rays forming the angle is the same.
The steps which are required for copying the angle are:
Draw a ray, of the copy of the angle as a ray with an endpoint, D.In the given angle ∠ABC, with the compass placed at point B, construct an arc that intersect the two sides of the given line (BA at point E, and BC at point F) by opening the compass to a radius, r.Place the compass at the point D on the line l and with the radius r from above, draw an arc (D, r) that intersects the line l at the point G.Place the compass at point E on line AB, and construct an arc passing through point F, therefore having radial length EF.Place the compass at point G and construct an arc with radial length EF that intersects the arc (D, r) at point H and draw a ray from the point D passing through point H to complete the construction.Hence, the correct order of steps for copying the angle ABC is BFCEDA.
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What is the square root of 81 as a fraction?
Answers
Answer: 9/1
Step-by-step explanation:
3 to the power of 2 divided by 3 plus 2 to the power of 2 times 7 minus 20 divided 5
Answers
Answer:
3^2/3+2^2x7-20/5
Do inverse operations first.
9/3+28-4
3+28-4
Answer = 27
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, the second mechanic worked for 5. Together they charged a total of 950$ What was the rate charged per hour by each mechanic if the sum of the two rates was 125$ per hour?
Answers
Answer:
Step-by-step explanation:
Let x = the hourly rate of the first mechanic and
y = the hourly rate of the second mechanic.
As far as the equation goes for the total amount charged:
10x + 5y = 950
As far as the equation goes for the sum of the 2 mechanics' rates:
x + y = 125
Solve the first equation for either x or y. I solved for y:
y = 125 - x
Now plug that into the first equation for y to get:
10x + 5(125 - x) = 950 and
10x + 625 - 5x = 950 and
5x = 325 so
x = 65
The first mechanic charges $65 per hour and the second mechanic charges
y = 125 - 65 so
the second mechanic charges $60 per hour.
HELP RN PLS
simplify (4^3)^5
Answers
Answer:
(4^3)5 = 4^15
hope this helpsStep-by-step explanation:
What is the long division answer for 19 on the outside (left) and 66 on the inside (right)?
Answers
Answer:
the answer is irrational (goes on forever) ... look at image...
I assume that the answer that you were to provide is
3 R 9 (3 remainder 9 )
or
[tex]3 \frac{9}{19}[/tex]
Step-by-step explanation:
Geometry
Topic: Measure Angles
Answers
Answer:
BOC = 42
Step-by-step explanation:
90 = 6z - 6 + 5z + 8
Combine common factors
90 = 11x + 2
Subtract 2 from both sides
88 = 11x
Divide both sides by 11
8 = x
Plug in 8 for x
6(8)- 6
48 - 6
42
Rewrite the following mathematical statement in your own words
Answers
Answer:
a set is a collection of elements. The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a
f: M ⇒ N is a function from M to N.
Given,
f: M ⇒ N
We need to describe this mathematical statement in our own words.
What is a function?A function is defined as a way where there is an input that it takes and produces an output.
The set from where the inputs come is called the Domain.
The set of outputs is called the Range.
We have,
f: M ⇒ N
Here
f is a function that takes input from the set M and its output belongs to set N( Natural number).
Here,
M is called the domain.
N is called the codomain.
Thus f: M ⇒ N is a function from M to N.
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What is the product of ¼, -½ and -¾?
a
0.0934
b
-0.6543
c
-0.09357
d
0.09375
Answers
Answer:
d. [tex]\displaystyle 0,09375[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3}{32} = [-\frac{3}{4}][-\frac{1}{2}][\frac{1}{4}] \\ \\ 0,09375 = \frac{3}{32}[/tex]
All you are doing is multiplying straight across!
I am joyous to assist you at any time.
Find the 7th term of the geometric sequence shown below
10x^3, 40x^8, 160x^13,…
Answers
Answer:
[tex]a_7=40960x^{33}[/tex]
Step-by-step explanation:
Geometric sequence has explicit form:
[tex]a_n=a \cdot r^{n-1}[/tex] where [tex]a[/tex] is first term and [tex]r[/tex] is the common ratio.
First term here is [tex]a=10x^3[/tex] and [tex]r[/tex] could be found by doing second term divided by first term, [tex]\frac{40x^8}{10x^3}=4x^5[/tex].
Therefore the [tex]n[/tex]th term is given by
[tex]a_n=10x^3 \cdot (4x^5)^{n-1}[/tex].
So the [tex]7[/tex]th term is given by
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex].
Let's simplify:
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex]
[tex]a_7=10x^3 \cdot (4x^5)^{6}[/tex]
[tex]a_7=10x^3 \cdot (4^6(x^5)^6)[/tex]
[tex]a_7=10x^3 \cdot (4096x^30)[/tex]
[tex]a_7=40960x^{33}[/tex]
Simplify. Express your answer as a single term using exponents.
1224. 1227
Answers
Answer: Um
Step-by-step explanation:
The ratio of Tahlia's wage to Brooke's wage is 5: 6. Brooke earns $915.60 per week. How much does Tahlia earn???
Answers
Answer:
Step-by-step explanation:
5/6 = tahlia / brook
5/6 = x / 915 Multiply both sides by 915
5*915/6 = x
4575 / 6 = x
x = 762.50
work out the value of v°
Answers
Answer:
v+91=180(being co-interior angle)
v=180-91
v=89,
Answer:
Step-by-step explanation:
v°+120°+91°+(180°-155°)=360°
v°+236°=360°
v°=360°-236°
v°=124°
Find the area of this circle please…Use 3 for pi
Answers
9514 1404 393
Answer:
432 ft²
Step-by-step explanation:
The radius is half the diameter.
r = (24 ft)/2 = 12 ft
Put the given numbers into the formula and do the arithmetic.
A = πr²
A = (3)(12 ft)² = 432 ft²
Pls please help me ASAP!!!
Answers
Answer:
z = 0
Step-by-step explanation:
3 (z + 7) = 21
3z + 21 = 21
3z = 0
z = 0
4 cm
10 cm
7 cm
12 cm
What is the area of the figure
Answers
Answer:
33cm
Step-by-step explanation:
add all
numbers..........................
Step-by-step explanation:
Which terms must be removed from 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 if the sum of the remaining terms is to equal 1?
Answers
1/4
Step-by-step explanation:
0.5+0.25+0.17+0.13+0.1+0.1=1.25
cual es la rais cuadrada de 2000
Answers
a fruitseller bought 50 kg of fruits. he sold 30 kg of fruits for the cost price of 35 kg of fruits and he sold the remaining quantity for the cost price of 16 kg of fruits. calculates his profit and loss percent in the total transactions
Answers
Step-by-step explanation:
let the price of fruits be X per kg
cp of 50kg of friuts =50x
he sells 30kg of fruits on its cp of 35 kg
cp of 30kg fruits=30x
sp of 30kg fruits=35x
remaing fruits is 20kg
he sells 20kg of fruits on cp of 16kg
cp of 20kg fruits=20x
sp of 20kg fruits =16x
total cp is =50x
total sp is =(35+16) =51x
sp>cp(it means profit)
profit =sp-cp
=51-50
= 1
profit%=gain/cp × 100
= 1/50×100
=2%
Thank you
Please mark me brainliest
round off 7284 to 1sf
Answers
Answer:
7000
Step-by-step explanation:
This is because when you round to the significant figure, you basically look at any digits at the start of the number, which isn't zero. In this case, it would be in the thousands place 7284. So you round 7284 to the nearest thousands, which, would be 7000
Un parque tiene una piscina en forma circular de 22 yd de diámetro. Un sendero en forma anular rodea la piscina. El sendero mide 6 yd de ancho. El sendero necesita una nueva capa de revestimiento. Si un galón de revestimiento cubre 4 yd2 ¿cuantos galones de revestimiento se necesitan?
Answers
Answer:
La verdad Nose la respuesta espero que alguien te ayude
12a+5b-3c, 6c-5a+8b, -8b+5c-7a
Answers
Answer:
11c-12a
Step-by-step explanation
Combine like terms
Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and points***
Answers
Answer:
1) 4900 is square
2) The greatest common factor 30 and 126 is 6. The GCF of 126 and 39204 is 18
3) i) 44100 ii) 48024900
Write in exponential form
ахахахахаха
Answers
Answer:
the exponential form of this is a to the power 6
I.e a⁶
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Find the value of
x for which ABCD
must be a
parallelogram.
24
2
6
12
Answers
Answer:
2
Step-by-step explanation:
Intersection point of diagonals is the mid point of each diagonal.So,
2x+8=6x
6x-2x=8
4x=8
x=8/4
x=2
Answer: x = 2
Concept:
There are many properties for parallelograms, however, here, we need to focus on one property about diagonals.
Diagonals of a parallelogram bisect each other.
Solve:
Given information
One side of the diagonal = 6x
The other side of diagonal = 2x + 8
Given expression deducted from the property of parallelogram
One side = Other side
Substitute values into the expression
6x = 2x + 8
Subtract 2x on both sides
6x - 2x = 2x + 8 - 2x
4x = 8
Divide 4 on both sides
4x / 4 = 8 / 4
[tex]\boxed{x=2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Help me please thank you
Answers
Answer:
19, 25, 32
Step-by-step explanation:
Find the difference within each number:
5 -> 7: + 2
7 -> 10: + 3
10 -> 14: + 4
With each difference, + 1 is added so we can infer the next difference will be + 5.
14 + 5 = 19
Next is + 6.
19 + 6 = 25
Now + 7.
25 + 7 = 32
The y-intercept of the line with equation 8x-4y=12
Answers
Answer:
y- intercept, x=0
8(0)-4y=12
y=-3
convert the following. a 1 day into second b 6.86 km into m
Answers
Answer:
a. there are 86400 seconds in a 24 hour day
b. to convert a km to a m you say
1000m is equivalent to 1 km
1000m:1km
x:6.86
x=6860m
I hope this helps
A banquet room has been set up with 10 tables that each have 8 seats. If 78 people show up for the banquet, how many empty seats will there be?
Answers
There would be 2 empty seats.
Explanation:
If we multiply 10x8 we would get 80. If 78 people show up, we would subtract 78 from 80 and our answer would be two.