Question

Simplify:

(i) $2^{\frac{3}{2}}{2}^{\frac{1}{5}}$ (ii) ${\left(\frac{1}{3^3}\right)}^7$ (iii) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}$ (iv) $7^{\frac{1}{2}}\cdot 8^{\frac{1}{2}}$

Answer 1

(i) $2^{\frac{3}{2}}{.2}^{\frac{1}{5}}$

By using property $X^a$. $X^b$=$X^{a+b}$

$=2^{\frac{3}{2}+\frac{1}{5}}=2^{\frac{17}{10}}$

(ii) ${\left(\frac{1}{3^3}\right)}^7$

By using property ${\left(\frac{x}{y}\right)}^a=\frac{x^a}{y^b}$

$=\frac{1}{(3^3{)}^7}$

$=\frac{1}{3^{21}}$ ...... $[\because (x^a{)}^b=x^{ab}]$

(iii) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}$

By using property $\frac{X^a}{X^b}=X^{a-b}$

$={11}^{\frac{1}{2}-\frac{1}{4}}={11}^{\frac{1}{4}}$

(iv) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$

$={56}^{\frac{1}{2}}$ ...... $[\because x^a{y}^a=(xy{)}^a]$