Chapter 4.2, Problem 52HP

To determine

To explain : the difference between the expressions

Answer to Problem 52HP

The difference of the expression $-3^4$ and $3^{-4}$ is that $-3$ multiply by itself four times and $\frac{1}{3}$ multiply by itself four times respectively .

Explanation of Solution

Given information :

  ${\left(-3\right)}^4$ and $3^{-4}$

The expression ${\left(-3\right)}^4$ has a base $-3$ and its power is 4, its means $-3$ multiply by itself four times.

The expression $3^{-4}$ means that the base is $\frac{1}{3}$ and its power is 4, its means $\frac{1}{3}$ multiply by itself four times.

Hence,the difference of the expression $-3^4$ and $3^{-4}$ is that $-3$ multiply by itself four times and $\frac{1}{3}$ multiply by itself four times respectively.