Chapter 9.3, Problem 30PPS

To determine

To find: The missing exponent in the given expression.

Answer to Problem 30PPS

  $1$

Explanation of Solution

Given information:

  $\left(5^x\right)\left(5^2\right)=5^3$

Calculation:

  $\begin{array}{l}\left(5^x\right)\left(5^2\right)=5^3\\ \Rightarrow 5^{x+2}=5^3\mathrm{...}\left(\text{Product of powers property}\right)\\ \Rightarrow x+2=3\\ \Rightarrow x=3-2\\ \Rightarrow x=1\end{array}$

The missing exponent is $1$