Chapter 9, Problem 12CR

To determine

To select the expression which has a value of 25.

Answer to Problem 12CR

Option C. ${125}^{\frac{2}{3}}$

Explanation of Solution

Given information :

Value of the expression is 25.

Option A. $5^{\frac{2}{3}}$

Option B. $5^{\frac{3}{2}}$

Option C. ${125}^{\frac{2}{3}}$

Option D. ${125}^{\frac{3}{2}}$

:

Option A. $5^{\frac{2}{3}}$

This expression signifies.

  $5^{\frac{2}{3}}={(\sqrt[3]{5})}^2$

Therefore, this option is rejected as it not equal to 25.

Option B. $5^{\frac{3}{2}}$

This expression signifies.

  $5^{\frac{3}{2}}={(\sqrt{5})}^3$

Therefore, this option is rejected as it not equal to 25.

Option C. ${125}^{\frac{2}{3}}$

This expression signifies.

  ${125}^{\frac{2}{3}}={(\sqrt[3]{125})}^2$

  $={(5)}^2$

Therefore, this option is selected as it is equal to 25.

Option D. ${125}^{\frac{3}{2}}$

This expression signifies.

  ${125}^{\frac{3}{2}}={(\sqrt{125})}^3$

Therefore, this option is rejected as it not equal to 25.