Question

Simplify and express in exponential form :
$\left[\right(3^2{)}^4\times \left({15}^3\right)]÷5^3$

Answer 1

$\frac{\left[\right(3^2{)}^4\times \left(15{)}^3\right]}{5^3}=\frac{3^8\times 5^3\times 3^3}{5^3}$ (using $(a^m{)}^n=a^{mn}$ and $(ab{)}^m-a^m{b}^m)$

$=3^8\times 5^{3-3}\times 3^3$ using $\frac{a^m}{a^n=a^{m-n}}$

$=3^8\times 3^3\times 5^0$

$=3^{8+3}\times 1$ since $a^0=1$

$=3^{11}$

$=3^{11}$ since $a^m\times a^n=a^{m+n}$