Question

Fill in the blanks to make the statement true: $432=2^4\times 3^{---}$.

Answer 1

Compute the power:

We can write that

$\begin{array}{rcl}432& =& 2\times 216\\ & =& 2\times 6\times 6\times 6\\ & =& 2\times 2\times 3\times 2\times 3\times 2\times 3\\ & =& 2\times 2\times 2\times 2\times 3\times 3\times 3\\ & =& 2^4\times 3^3\end{array}$

Hence, the required statement is $432=2^4\times 3^{\underline{3}}$.