Question

Find the answer for $64$ power $\frac{1}{6}$.

Answer 1

Step 1: Writing using prime factors:

First, we can write using prime factors as

$\begin{array}{rcl}64& =& 8\times 8\\ & =& 4\times 2\times 4\times 2\\ & =& 2\times 2\times 2\times 2\times 2\times 2\end{array}$

$=\begin{array}{rcl}& & 2\end{array}\begin{array}{rcl}& & \end{array}$ . . . . . . $\left(1\right)$

Step 2: Compute the required value:

Using equation $\left(1\right)$, we can write as

$\therefore ,{\left(64\right)}^{\frac{1}{6}}={\left(2^6\right)}^{\frac{1}{6}}$

$=2^{6\times \frac{1}{6}}[\because {\left(a^m\right)}^n=a^{mn}]$

$=2^1$

$=2$

Hence, the required answer is ${\left(64\right)}^{\frac{1}{6}}=2$.