Question

Find the value of the following

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

$b\left)\right(0.000064{)}^{\frac{5}{4}}\times (0.04{)}^{\frac{5}{4}}$ [4 MARKS]

Answer 1

Application: 2 Marks Each

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

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

$=(5\times 5^3{)}^{\frac{1}{4}}$

$=5^{4\times \frac{1}{4}}$

$=5$


$b\left)\right(\frac{64}{1000000}{)}^{\frac{5}{4}}\times (\frac{4}{100}{)}^{\frac{5}{4}}$

$=(\frac{2^6}{{10}^6}{)}^{\frac{5}{4}}.(\frac{2^2}{{10}^2}{)}^{\frac{5}{4}}$

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

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

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

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

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

$=2^{10}.2^{-10}.5^{-10}$

$=5^{-10}$