Question

Evaluate the following : ${25}^{\frac{3}{2}}\times {16}^{-\frac{3}{4}}\times 5^{-2}\times {1024}^{\frac{3}{2}}$

Answer 1

$(25{)}^{\frac{3}{2}}\times (16{)}^{\frac{-3}{4}}\times 5^{-2}\times (1024{)}^{\frac{2}{3}}$

$\Rightarrow (5^2{)}^{\frac{3}{2}}\times (2^4{)}^{\frac{-3}{4}}\times 5^{-2}\times (2^{10}{)}^{\frac{3}{2}}$

$\Rightarrow 5^3\times 2^{-3}\times 5^{-2}\times 2^{15}$

$\Rightarrow 5^{(3-2)}\times 2^{(-3+15)}$

$\Rightarrow 5\times 2^{12}$

$\Rightarrow 20480$

$\therefore {25}^{\frac{3}{2}}\times {16}^{\frac{-3}{4}}\times 5^{-2}\times (1024{)}^{\frac{3}{2}}=20480$.