Question

Write in single exponent form:

$5^2\times 3^2$

Answer 1

In $5^2\times 3^2$, there are different bases but the exponents are same.

So, for any non-zero integers $a,b$ where $m$ is any whole number,

$a^m\times b^m={\left(ab\right)}^m$

$5^2\times 3^2$$=(5\times 5)\times (3\times 3)$ (Here $a=5,b=3,m=2$)

$=(5\times 3)\times (5\times 3)$

$={(5\times 3)}^2$

$={15}^2$

Therefore, $5^2\times 3^2$$={15}^2$