Question

a) the value of (32)^1/5 is----
b)the value of(0.001)^1/3 is------
c) the value of (256/625)^-1/4 is------​

Answer 1

a) The value of (32)^1/5 is 2

b) The value of(0.001)^1/3 is 0.1

c) The value of (256/625)^-1/4 is 4/5

Step by step

a) We have

$\bold{ {32}^{ \frac{1}{5} } }$

$= ( {2}^{5} ) {}^{ \frac{1}{5} }$

$= 2$

$b) \: 0.001=\frac{1}{1000}=\frac{1 \times 1 \times 1}{10 \times 10 \times 10}=\frac{1^{3}}{10^{3}}$

$(0.001)^{\frac{1}{3}}=\left(\frac{1^{3}}{10^{3}}\right)^{\frac{1}{3}}$

$\begin{gathered}\begin{array}{l}{=\frac{1}{10}} \\ {=0.1}\end{array}\end{gathered}$

$\bold{The \: value \: of \: \bold{(0.001)^{\frac{1}{3}}}} \: \bold{is} \: \bold{0.1}$

$\begin{gathered} \\c) \: (\frac{256}{625} ) ^{ \frac{1}{4} } \\ = [ ( \frac{4}{5} )^{4}] ^{ \frac{1}{4} } \\ = (\frac{4}{5} ) ^{4 \times \frac{1}{4} } \\ = \frac{4}{5} \end{gathered}$