Question

Simplify and express the following in exponential form:
$\left[{\left(5^2\right)}^3\right]÷5^7$

Answer 1

$\left[{\left(5^2\right)}^3\right]÷5^7=[5^6\times 5^4]+5^7$
$=\left[5^{6+4}\right]÷5^7=5^{10}÷5^7$
$=5^{10-7}=5^3$
$[\because {\left(a^m\right)}^n=a^{mn}]$
$[\because a^m\times a^v=a^{m+v}][\because a^m÷a^v=a^{m-v}]$