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 :)
Twenty percent of 80<span> is 16.
Hoped I helped!</span>
Step-by-step explanation:
To calculate the mean, we do the the total divided by the number of values. With 6 values, for the average to be 8, the total needs to be 48. The current total is 41, so Chicken Wings needs to be 7, because 48-41=7
Answer
Find out the how much fertilizer will Timothy need for two fields, one that is 22.5 acres and one that is 38.25 acres .
To proof
As given
Timothy is putting fertilizer on a field after planting some crops
The directions on the barrel state to use 0.75 quarts for each acre of land.
fertilizer will Timothy need for 22.5 acres = 22.5 × 0.75
= 16.875 quarts
fertilizer will Timothy need for 38.25 acres = 38.25×0.75
= 28.6875 quarts
total fetilizer Timothy need for two fields = 16.875 + 28.6875
= 45.5625
= 45.6 ( approx )quarts
Therefore the total fertilizer will Timothy need for two fields be 45.6 ( approx )quarts .
Hence proved
There are essentially two ways that I know to solve this.
One is to guess.
The other is to find the prime factors of 96. For an integer to be a perfect square, each prime factor has to occur an even number of time. Therefore k would need to be the product of whatever primes occur in 96 an odd number of times.
Given that 9+6 is divisible by 3, we know that 96 is divisible by 3. Doing the division, we find that 96 = 3 * 32.
The prime factor 3 only occurs once. Therefore k must be a multiple of 3.
32 is 2 raised to the 5th power. This is an odd number of 2’s. We need one more. Therefore k must be a multiple of 2.
Therefore the smaller possible value of k is 6.
96 * 6 is a perfect square. It is the same as 64 * 9, or 24 * 24.
Hope it helps!