Question

Express in exponential form: ${\left(\frac{256}{84}\right)}^{\frac{5}{4}}$.

Answer 1

${\left(\frac{256}{84}\right)}^{5/4}=$ $\frac{(2^8{)}^{5/4}}{(2^2\times 7\times 3{)}^{5/4}}$ using $(a^m{)}^n=a^{mn}$

$=\frac{2^{8\times 5/4}}{2^{2\times 5/4}\times 7^{5/4}\times 3^{5/4}}$

$=2^{\frac{40-10}{4}}\cdot 7^{-5/4}\times 3^{-5/4}$

$=\frac{2^{30/4}}{(21{)}^{5/4}}=\frac{2^{15/2}}{(21{)}^{5/4}}$.