Question

What is the value of $-3$ to the power $-4$?

Answer 1

Determine the value of $-3$ to the power $-4$.

Calculate the value of $-3^{-4}$:

$\begin{array}{rcl}-3^{-4}& =& \frac{1}{-3^4}\left[\because a^{-m}=\frac{1}{a^m}\right]\\ & \Rightarrow & -3^{-4}=\frac{1}{-3\times -3\times -3\times -3}\\ & \Rightarrow & -3^{-4}=\frac{1}{81}\end{array}$

Therefore, the value of $-3$ to the power $-4$ is $\frac{1}{81}$.