Chapter 7.1, Problem 43PPE

To determine

To Evaluate: The expression $r^{-4}{s}^2$ for $r=-3$ and $s=5$

Answer to Problem 43PPE

The required solution is $\frac{25}{81}$

Explanation of Solution

Given information:

  $r^{-4}{s}^2$

  $r=-3$ and $s=5$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer.

Zero as an Exponent:

  $a^0=1$

Where a is a non-zero number.

Calculation:

  $r^{-4}{s}^2$

Applying Negative Exponent concept

  $=\frac{s^2}{r^4}$

Substituting the known value:

  $\begin{array}{l}=\frac{5^2}{{\left(-3\right)}^4}\\ =\frac{25}{81}\end{array}$