Chapter 4.6, Problem 41E

To determine

To prove that $6^{-2}$ is different from $6^2$

Answer to Problem 41E

  $6^{-2}\ne 6^2$

Explanation of Solution

Given information: $6^{-2}and{6}^2$

$6^{-2}and{6}^2$

To prove that both these terms are different, expand both the terms.

  $6^{-2}=\frac{1}{6^2}$

Which further becomes

  $=\frac{1}{36}$

And Right hand side is

  $6^{-2}$

So

  $6^2$ is not equal to $6^2$

Since the exponent in the first term was negative, the value of 36 would come onto the denominator.

Hence both these terms are different.