<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
Answer:
C
Step-by-step explanation:
Gross taxable Income = $ 1,166
Rate of Income tax = 30%
Amount of income tax = 30 % of 1,166
= 
=$339.6
≅$340
A) 672750
B) 68250
C) 2960100
ExplanationA) We have 26 letters from which to choose 4, and 10 digits from which to choose 2:
B) We have 26 letters from which to choose 2, and 10 digits from which to choose 4:
C) We have 26 letters from which to choose 5, and 10 digits from which to choose 2:
Answer:
0.1x+0.15(50-x)= 50*0.12
Step-by-step explanation:
50 ml of 12% solution has 50*0.12 ml of alcohol
x ml of 10% solution has x*0.1 ml of alcohol
(50-x) ml of 15% solution has (50-x)*0.15 ml of alcohol
The equation to solve is:
Let's convert all volumes into pint:
1 Quart = 2 pints → 3.5 quart of strawberry = 2 x 3.5 = 7 pints Strawberry
1 Gallon = 8 pints →1.25 Ga. water = 1.25 x 8 = 10 pints Water
2 pints of limonade = 2 pints of limonade
Add up all pints Total = 7+10+2 = 19 pints of smoothie
Or in quart 9.5
Or in Gal 2.375
