Chapter 7.1, Problem 40PPE

To determine

To Evaluate: The expression $\frac{s^0}{r^{-2}}$ for $r=-3$ and $s=5$

Answer to Problem 40PPE

The required solution is $9$

Explanation of Solution

Given information:

  $\frac{s^0}{r^{-2}}$

  $r=-3$ 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:

  $\begin{array}{l}\frac{s^0}{r^{-2}}\\ =s^0÷r^{-2}\end{array}$

Applying Negative Exponent concept

  $=s^0÷\frac{1}{r^2}$

Multiplying the reciprocal of $\frac{1}{r^2}$

  $=s^0\cdot r^2$

Applying Negative Exponent concept

  $\begin{array}{l}=1\cdot r^2\\ =r^2\end{array}$

Substituting the known value:

  $\begin{array}{l}={\left(-3\right)}^2\\ =9\end{array}$