Simplify:"

Given,

[(3−1​)8÷(3−1​)5]−[(3−1​)5÷(3−1​)3]

We know that,

$a^{m} \div a^{n} =a^{m-n}$

We have to simplify the given expression.

$\left[\left(\frac{-1}{3}\right)^{8} \div \left(\frac{-1}{3}\right)^{5}\right] -\left[\left(\frac{-1}{3}\right)^{5} -\left(\frac{-1}{3}\right)^{3}\right] =(\left(\frac{-1}{3}\right)^{8-5} -\left(\frac{-1}{3}\right)^{5-3} =\left(\frac{-1}{3}\right)^{3} -\left(\frac{-1}{3}\right)^{2} =\frac{-1}{27} -\frac{1}{9} =\frac{-1\times 1-1\times 3}{27} =\frac{-1-3}{27} =\frac{-4}{27}$

$={\left(\frac{−1}{3}\right)}^3−{\left(\frac{−1}{3}\right)}^2$

$=\frac{−1}{27}−\frac{1}{9}$

$=\frac{−1\times 1−1\times 3}{27}$

$=\frac{−1−3}{27}$

$=\frac{−4}{27}$ .

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Updated on: 10-Oct-2022

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