Answer:
12.083
Explanation:
Plug into a calculator.
<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)
Answer:
Let 'x' and 'y' be two different numbers.
Leila says that 75% of a number will always be greater than 50% of a number. The inequality that represents this statement is the following:
0.75x > 0.5y
Let x = 100 and y=200. We have that:
0.75(100) > 0.5(200)
75 > 100 ❌ INCORRECT ❌
Given that we found a case in which 75% of a number is not greater than 50% of a number, we can conclude that Leila's claim is incorrect.
Answer:
I) 32.5
ii) 100.1
Step-by-step explanation:
I) 1056.25 = √1056.25
= 32.5
ii) 10020.01= √10020.01
=100.1