Question

If $12500=5^a\times 2^b$, Find $a$ and $b$.

Answer 1

Solve for the factors of $12500$ and group them.

Given, $12500=5^a\times 2^b$

The factors of $12500$ are

$\begin{array}{rcl}12500& =& 5\times 5\times 5\times 5\times 5\times 2\times 2\\ & =& 5^5\times 2^2\end{array}$.

Comparing it with given data.

$\begin{array}{cc}& 12500=5^a\times 2^b\\ \Rightarrow & 5^5\times 2^2=5^a\times 2^b\end{array}$

$\therefore a=5,b=2$

Therefore, the values of $a$ and $b$ are $5$ and $2$ respectively.