Question

Write in single exponent form:

$6^4\times {10}^4$

Answer 1

In $6^4\times {10}^4$, there are different bases but the exponents are same.

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

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

$6^4\times {10}^4$$=(6\times 6\times 6\times 6)\times (10\times 10\times 10\times 10)$ (Here $a=6,b=10,m=4$)

$=(6\times 10)\times (6\times 10)\times (6\times 10)\times (6\times 10)$

$={(6\times 10)}^4$

$={60}^4$

Therefore, $6^4\times {10}^4$$={60}^4$