<u>ANSWER</u>
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20-%209%20%7Ba%7D%5E%7B3%7D%20%7Bb%7D%5E%7B2%7D%20)
<u>EXPLANATION</u>
We want to find the cube root of

We express this symbolically as:
![\sqrt[3]{- 729 {a}^{9} {b}^{6} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20)
The expression under the radical called the radicand.
We need to express this radical in exponential form using the property,
![{x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} }](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%20%7D%20%20%3D%20%20%5Csqrt%5Bn%5D%7B%20%7Bx%7D%5E%7Bm%7D%20%7D%20)
Applying this rule gives us:
![\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20729%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20)
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20%7B9%7D%5E%7B3%7D%20%20%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20)
Recall that

We apply this rule on the RHS to get,
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20%28%7B-%20%7B9%7D%5E%7B3%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%7Ba%7D%5E%7B9%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%7Bb%7D%5E%7B6%20%5Ctimes%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%7D%29)
This simplifies to
![\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%20729%7Ba%7D%5E%7B9%7D%20%20%7Bb%7D%5E%7B6%7D%20%7D%20%20%3D%20%20-%209%20%7Ba%7D%5E%7B3%7D%20%7Bb%7D%5E%7B2%7D%20)
I believe the answer would be 49.64 because if you add them together 22.65+33.31 = 55.96 x .10 = 5.60 55.96-5.60 = $49.64
Answer:
376 squared inches for the hole bird house, 60 for the side with the whole.
Step-by-step explanation:
1 side is 60 inches squared, another is 48 inches squared, and another is 80 inches squared, and there are two of each side so you get 120+96+160= 376.
Answer:
3m = 18
Step-by-step explanation:
9 + 12m = 6 + 15(m - 1)
9 + 12m = 6 + 15m - 15
3m = 18
Answer:
The domain of the function (cd)(x) will be all real values of x except x = 2.
Step-by-step explanation:
The two functions are
and d(x) = x + 3
So, (cd)(x) = 
Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.
Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)