Question

simplify:
i) $(1^3+2^3+3^3{)}^{1/2}$
ii) ${\left(\frac{81}{16}\right)}^{3/4}\times {\left(\frac{25}{9}\right)}^{-3/2}$

Answer 1

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

on simplifying

$\Rightarrow (1+8+27{)}^{\frac{1}{2}}$

$(36{)}^{\frac{1}{2}}$

$\left[\right(6){]}^{\frac{1}{2}}=6$

(ii) $(\frac{81}{16}{)}^{\frac{3}{4}}\times (\frac{25}{9}{)}^{\frac{-3}{2}}$

$\Rightarrow$ On simplifying we get

$(\frac{(3{)}^4}{(2{)}^4}{)}^{\frac{3}{4}}\times [(\frac{5}{3}{)}^2{]}^{\frac{-3}{2}}$

$\Rightarrow (\frac{3}{2}{)}^3\times (\frac{5}{3}{)}^{-3}$

$\Rightarrow (\frac{3}{2}{)}^3\times (\frac{3}{5}{)}^3=\frac{(3{)}^6}{10}$

$\Rightarrow \frac{729}{10}$