Question

What is the value of $\frac{1}{2}$ to the power $-6$?

Answer 1

Determine the value of $\frac{1}{2}$ to the power $-6$.

In mathematical terms, $\frac{1}{2}$ to the power $-6$ as ${\left(\frac{1}{2}\right)}^{-6}$.

Apply the negative property of exponents: $a^{-m}=\frac{1}{a^m}$, where $m$ is any number and $a\ne 0$.

$\begin{array}{rcl}{\left(\frac{1}{2}\right)}^{-6}& =& \frac{1}{{\left(\frac{1}{2}\right)}^6}\\ & \Rightarrow & {\left(\frac{1}{2}\right)}^{-6}=2^6\\ & \Rightarrow & {\left(\frac{1}{2}\right)}^{-6}=64\end{array}$

Hence, the value is $\begin{array}{rcl}{\left(\frac{1}{2}\right)}^{-6}& =& 64\end{array}$.