Simplify and express in exponential form:

$\left[\right(5^2{)}^3\times 5^4]÷5^7$ [3 MARKS]

Steps: 2 Marks
Answer: 1 Mark

$=\left[\right(5^2{)}^3\times 5^4]÷5^7$

$=[5^6\times 5^4]÷5^7$ $[\because (a^m{)}^n=a^{m\times n}]$

$=\left[5^{6+4}\right]÷5^7$ $[\because a^m\times a^n=a^{m+n}]$

$=5^{10}÷5^7$

$=5^{10-7}$ $[\because a^m÷a^n=a^{m-n}]$

$=5^3$