Question

Evaluate $3\times {\left(9\right)}^{\frac{5}{2}}\times {\left(9\right)}^{\frac{-1}{2}}$

Answer 1

Given:

$3\times {\left(9\right)}^{\frac{5}{2}}\times {\left(9\right)}^{\frac{-1}{2}}$
$=3\times {\left(3^2\right)}^{\frac{5}{2}}\times {\left(3^2\right)}^{\frac{-1}{2}}$

$=3\times {\left(3\right)}^{2\times \frac{5}{2}}\times {\left(3\right)}^{2\times \frac{-1}{2}}$ [Since, Power of power rule:$(a^m{)}^n=a^{mn}$]

$=3\times 3^5\times 3^{-1}$
$=3^{1+5-1}$ [Since, Product rule: $a^m\times a^n\times a^p=a^{m+n+p}$]
$=3^5$

$=3\times 3\times 3\times 3\times 3$

$=243$

$\therefore 3\times {\left(9\right)}^{\frac{5}{2}}\times {\left(9\right)}^{\frac{-1}{2}}=243$