Question

The value of $(0.000064{)}^{\frac{5}{4}}\times (0.04{)}^{\frac{5}{4}}$ is

• A. $2^{10}.0^{10}$
• B. $2^{10}.{10}^{-10}$
• C. $2^{-10}.{10}^{10}$
• D. None of these

Answer 1

The correct option is B $2^{10}.{10}^{-10}$

${\left(\frac{64}{1000000}\right)}^{\frac{5}{4}}\times {\left(\frac{4}{100}\right)}^{\frac{5}{4}}$$={\left(\frac{2^6}{{10}^6}\right)}^{\frac{5}{4}}{\left(\frac{2^2}{{10}^2}\right)}^{\frac{5}{4}}$

$={\left(\frac{2^6\times 2^2}{{10}^6\times {10}^2}\right)}^{\frac{5}{4}}$

$={\left(\frac{2^8}{{10}^6}\right)}^{\frac{5}{4}}$

$=\frac{2^{8\times \frac{5}{4}}}{{10}^{8\times \frac{5}{4}}}$

$=\frac{2^{10}}{{10}^{10}}=2^{10}.{10}^{-10}$