Question

Evaluate (i) $(1^3+2^3+3^3{)}^{\frac{1}{2}}$ (ii) ${\left[5{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^3\right]}^{\frac{1}{4}}$ (iii) $\frac{2^0+7^0}{5^0}$ (iv)${\left[\right(16{)}^{\frac{1}{2}}]}^{\frac{1}{2}}$

Answer 1

$\left(i\right)(1^3+2^3+3^3{)}^{\frac{1}{2}}=(1+8+27{)}^{\frac{1}{2}}={36}^{\frac{1}{2}}=\sqrt{36}=6$

$\left(ii\right)\left[5\right(8^{\frac{1}{3}}+{27}^{\frac{1}{3}}{)}^3{]}^{\frac{1}{4}}=\left[5\right(2+3{)}^3{]}^{\frac{1}{4}}=5^{\frac{4}{4}}=5$

$\left(iii\right)\frac{2^0+7^0}{5^0}=\frac{(1+1)}{1}=2$

$\left(iv\right)\left[\right(16{)}^{\frac{1}{2}}{]}^{\frac{1}{2}}=4^{\frac{1}{2}}=2$