Question

Find the value of each of the following
$\left(i\right)5^{\frac{1}{2}}\times 5^{\frac{3}{2}}$
$\left(ii\right)7^{\frac{4}{3}}\times 7^{\frac{2}{3}}$

• A. $25,50,36$
• B. $25,49,36$
• C. $25,36,49$
• D. $22,49,33$

Answer 1

The correct option is B $25,49,36$

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

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

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

$=5^2$

$=5\times 5=25$


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

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

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