Chapter 13.3, Problem 75STP

To determine

To find: Evaluate each expression.

Answer to Problem 75STP

  ${25}^{-\frac{5}{2}}=\frac{1}{3125}$

Explanation of Solution

Given information:

  ${25}^{-\frac{5}{2}}$

Given

  ${25}^{-\frac{5}{2}}$

  $\begin{array}{l}{25}^{-\frac{5}{2}}={\left(5^2\right)}^{-\frac{5}{2}}\\ \Rightarrow {25}^{-\frac{5}{2}}=5^{2\times \frac{-5}{2}}\\ \Rightarrow {25}^{-\frac{5}{2}}=5^{-5}\\ \Rightarrow {25}^{-\frac{5}{2}}=\frac{1}{5^5}\\ \Rightarrow {25}^{-\frac{5}{2}}=\frac{1}{3125}\end{array}$

Therefore,

  ${25}^{-\frac{5}{2}}=\frac{1}{3125}$