Our first expression is
. Upon distributing the exponent 4 on all the terms, we get:
![(2p^{-3} q^{8} )^{4}=2^{4}(p^{-3})^{4}(q^{8})^{4}=16p^{-12}q^{32}=\frac{16q^{32}}{p^{12}}](https://tex.z-dn.net/?f=%282p%5E%7B-3%7D%20q%5E%7B8%7D%20%29%5E%7B4%7D%3D2%5E%7B4%7D%28p%5E%7B-3%7D%29%5E%7B4%7D%28q%5E%7B8%7D%29%5E%7B4%7D%3D16p%5E%7B-12%7Dq%5E%7B32%7D%3D%5Cfrac%7B16q%5E%7B32%7D%7D%7Bp%5E%7B12%7D%7D)
Therefore, your answer is correct for this part. :)
Second expression is
. Upon distributing the exponent -2 on all the terms, we get:
![(2m^{-4}n^{5})^{-2}=2^{-2}(m^{-4})^{-2}(n^{5})^{-2}=2^{-2}m^{8}n^{-10}=\frac{m^{8}}{4n^{10}}](https://tex.z-dn.net/?f=%282m%5E%7B-4%7Dn%5E%7B5%7D%29%5E%7B-2%7D%3D2%5E%7B-2%7D%28m%5E%7B-4%7D%29%5E%7B-2%7D%28n%5E%7B5%7D%29%5E%7B-2%7D%3D2%5E%7B-2%7Dm%5E%7B8%7Dn%5E%7B-10%7D%3D%5Cfrac%7Bm%5E%7B8%7D%7D%7B4n%5E%7B10%7D%7D)
Your second answer is correct too.
Our third expression is
. Upon distributing the exponent 2 on all the terms, we get:
![2(5g^{-4}h^{-6})^{2}=2(5^{2})(g^{-4})^{2}(h^{-6})^{2}=2(25)g^{-8}h^{-12}=\frac{50}{g^{8}h^{12}}](https://tex.z-dn.net/?f=2%285g%5E%7B-4%7Dh%5E%7B-6%7D%29%5E%7B2%7D%3D2%285%5E%7B2%7D%29%28g%5E%7B-4%7D%29%5E%7B2%7D%28h%5E%7B-6%7D%29%5E%7B2%7D%3D2%2825%29g%5E%7B-8%7Dh%5E%7B-12%7D%3D%5Cfrac%7B50%7D%7Bg%5E%7B8%7Dh%5E%7B12%7D%7D)
This one is not correct. Your answer would have been correct, if the exponent were -2 instead of 2 in this part.
Our forth and last expression is
. Upon distributing the exponent -5 on all the terms inside the parenthesis, we get:
![4(2c^{-3}d^{6})^{-5}=4(2^{-5})(c^{-3})^{-5}(d^{6})^{-5}=\frac{4}{2^{5}}(c^{15})(d^{-30})=\frac{4c^{15}}{32d^{30}}=\frac{c^{15}}{8d^{30}}](https://tex.z-dn.net/?f=4%282c%5E%7B-3%7Dd%5E%7B6%7D%29%5E%7B-5%7D%3D4%282%5E%7B-5%7D%29%28c%5E%7B-3%7D%29%5E%7B-5%7D%28d%5E%7B6%7D%29%5E%7B-5%7D%3D%5Cfrac%7B4%7D%7B2%5E%7B5%7D%7D%28c%5E%7B15%7D%29%28d%5E%7B-30%7D%29%3D%5Cfrac%7B4c%5E%7B15%7D%7D%7B32d%5E%7B30%7D%7D%3D%5Cfrac%7Bc%5E%7B15%7D%7D%7B8d%5E%7B30%7D%7D)
Therefore, your answer for this part is also correct.
Looking at your work, I don't think you made a mistake in number 3 also, probably mis-typed the question while writing here :)
Answer:
![\frac{2}{13}/\frac{2}{3}\\ \frac{2}{13}*\frac{3}{2}\\\frac{3}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B13%7D%2F%5Cfrac%7B2%7D%7B3%7D%5C%5C%20%20%5Cfrac%7B2%7D%7B13%7D%2A%5Cfrac%7B3%7D%7B2%7D%5C%5C%5Cfrac%7B3%7D%7B13%7D)
Step-by-step explanation:
Rewriting this equation in slope-intercept form:
y = (-3/4)x + 3
The slope is now the coefficient of the “x” term.
So the slope of this line is -3/4, so a parallel line must also have a slope of -3/4.
You can factorize to simplify the expression
The answer would be,
![4(2x - y)](https://tex.z-dn.net/?f=4%282x%20-%20y%29)
Hope this helped
:D
Answer:
A.![977\ feet^{2}](https://tex.z-dn.net/?f=977%5C%20feet%5E%7B2%7D)
Step-by-step explanation:
Given:-
Actual size of billboard,
Width(w)=2.61 inches
Length(l)=6.14 inches
Now,
To create a billboard in scale 1 inch to 7.81 feet,
this means,
1 inch=7.81 feet --------------(as per scale)
So,
2.61 inches=2.61
7.81
2.61 inches=20.38 feet (Width)
6.14 inches=6.14
7.81
6.14 inches=47.95 feet (Length)
Now the area of billboard as per scale is:
![Area=Width\times Length](https://tex.z-dn.net/?f=Area%3DWidth%5Ctimes%20Length)
![Area=20.38\times 47.95](https://tex.z-dn.net/?f=Area%3D20.38%5Ctimes%2047.95)
![Area=977.22\ square\ feet](https://tex.z-dn.net/?f=Area%3D977.22%5C%20square%5C%20feet)
![Area=977\ feet^{2}](https://tex.z-dn.net/?f=Area%3D977%5C%20feet%5E%7B2%7D)
Therefore billboard nearest area is A. 977![feet^{2}](https://tex.z-dn.net/?f=feet%5E%7B2%7D)