Question

Find the value of each of the following [4 MARKS]

$\left(i\right)(5{)}^{\frac{1}{2}}\times (5{)}^{\frac{3}{2}}$

$\left(ii\right)(7{)}^{\frac{4}{3}}\times (7{)}^{\frac{2}{3}}$

$\left(iii\right)4\times (9{)}^{\frac{5}{2}}\times (9{)}^{-\frac{3}{2}}$

Answer 1

Concept: 1 Mark
Application: 1 Mark each

$\left(i\right)(5{)}^{\frac{1}{2}}\times (5{)}^{\frac{3}{2}}$

$=(5{)}^{\frac{1}{2}+\frac{3}{2}}$ $[Using:x^a\times x^b=x^{a+b}]$

$=(5{)}^{\frac{1+3}{2}}$

$=(5{)}^{\frac{4}{2}}$

$=(5{)}^2$

$=5\times 5=25$


$\left(ii\right)(7{)}^{\frac{4}{3}}\times (7{)}^{\frac{2}{3}}$

​​​​​​$=(7{)}^{\frac{4}{3}+\frac{2}{3}}$ $[Using:x^a\times x^b=x^{a+b}]$

$=(7{)}^{\frac{6}{3}}$

$=7^2$
$=7\times 7$
$=49$


$\left(iii\right)4\times (9{)}^{\frac{5}{2}}\times (9{)}^{-\frac{3}{2}}$

$=4\times \left(9{)}^{\frac{5}{2}+(-\frac{3}{2})}\right[Using:x^a\times x^b=x^{a+b}]$

$=4\times (9{)}^{\frac{5}{2}-\frac{3}{2}}$

$=4\times (9{)}^{\frac{5-3}{2}}$

$=4\times 9^{\frac{2}{2}}$

$=4\times 9$

$=36$