Simplify: $ 4 \times(0.81)^{-\frac{1}{2}} \times\left[(0.064)^{\frac{1}{3}}+(0.0625)^{\frac{1}{4}}\right] $

Given:

\( 4 \times(0.81)^{-\frac{1}{2}} \times\left[(0.064)^{\frac{1}{3}}+(0.0625)^{\frac{1}{4}}\right] \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$a^{-m}=\frac{1}{a^m}$

Therefore,

$ \begin{array}{l}
4\times ( 0.81)^{-\frac{1}{2}} \times \left[( 0.064)^{\frac{1}{3}} +( 0.0625)^{\frac{1}{4}}\right] =4\times \left(\frac{81}{100}\right)^{-\frac{1}{2}} \times \left[\left(\frac{64}{1000}\right)^{\frac{1}{3}} +\left(\frac{625}{10000}\right)^{\frac{1}{4}}\right]\\
\\
=4\times \left(\frac{100}{81}\right)^{\frac{1}{2}} \times \left[\left(\frac{4^{3}}{10^{3}}\right)^{\frac{1}{3}} +\left(\frac{5^{4}}{10^{4}}\right)^{\frac{1}{4}}\right]\\
\\
=4\times \left(\frac{10^{2}}{9^{2}}\right)^{\frac{1}{2}} \times \left[\left(\frac{4}{10}\right)^{3\times \frac{1}{3}} +\left(\frac{5}{10}\right)^{4\times \frac{1}{4}}\right]\\
\\
=4\times \left(\frac{10}{9}\right)^{2\times \frac{1}{2}} \times \left[\left(\frac{4}{10}\right) +\left(\frac{5}{10}\right)\right]\\
\\
=\frac{4\times 10}{9} \times \left(\frac{4+5}{10}\right)\\
\\
=\frac{40}{9} \times \frac{9}{10}\\
\\
=4
\end{array}$ 

Therefore,

\( 4 \times(0.81)^{-\frac{1}{2}} \times\left[(0.064)^{\frac{1}{3}}+(0.0625)^{\frac{1}{4}}\right] \)$=4$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

34 Views

Kickstart Your Career

Get certified by completing the course

Get Started