Question

Answer this question​

Answer 1

Solution:

Given to evaluate,

$\tt = ( {4}^{ - 1} - {8}^{ - 1} ) \div \bigg( \dfrac{2}{3} \bigg)^{ - 2}$

We know that,

$\tt \longrightarrow {x}^{ - 1} = \dfrac{1}{x}$

So, after simplifying, we get,

$\tt = \bigg(\dfrac{1}{4} - \dfrac{1}{8} \bigg) \div \bigg( \dfrac{3}{2} \bigg)^{2}$

$\tt = \bigg( \dfrac{2 - 1}{8} \bigg) \div \bigg( \dfrac{3}{2} \bigg)^{2}$

$\tt = \dfrac{1}{8} \div \dfrac{9}{4}$

$\tt = \dfrac{1}{8} \times \dfrac{4}{9}$

$\tt = \dfrac{1}{2} \times \dfrac{1}{9}$

$\tt = \dfrac{1}{18}$

$\tt = {18}^{ - 1}$

Which is our required answer.

Answer:

• Result after simplification = 1/18.