Question

{(1/3)^-2 - (1/2)^-3}÷(1/4)^-2

Answer 1

hope it will helps you.......

Answer 2

$\displaystyle \sf \bigg \{ {\bigg( \frac{1}{3} \bigg)}^{ - 2} - {\bigg( \frac{1}{2} \bigg)}^{ - 3} \bigg \} \div {\bigg( \frac{1}{4} \bigg)}^{ - 2} = \frac{1}{16}$

Given :

$\displaystyle \sf \bigg \{ {\bigg( \frac{1}{3} \bigg)}^{ - 2} - {\bigg( \frac{1}{2} \bigg)}^{ - 3} \bigg \} \div {\bigg( \frac{1}{4} \bigg)}^{ - 2}$

To find :

To simplify the expression

Formula :

We are aware of the formula on indices that :

$\sf{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf \bigg \{ {\bigg( \frac{1}{3} \bigg)}^{ - 2} - {\bigg( \frac{1}{2} \bigg)}^{ - 3} \bigg \} \div {\bigg( \frac{1}{4} \bigg)}^{ - 2}$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf \bigg \{ {\bigg( \frac{1}{3} \bigg)}^{ - 2} - {\bigg( \frac{1}{2} \bigg)}^{ - 3} \bigg \} \div {\bigg( \frac{1}{4} \bigg)}^{ - 2}$

$\displaystyle \sf = \bigg \{ {\bigg( {3}^{ - 1} \bigg)}^{ - 2} - {\bigg( {2}^{ - 1} \bigg)}^{ - 3} \bigg \} \div {\bigg( {4}^{ - 1} \bigg)}^{ - 2}$

$\displaystyle \sf = \bigg \{ {3}^{( - 1) \times ( - 2)} - {( 2 )}^{ (- 1) \times ( - 3)} \bigg \} \div {4}^{ ( - 1) \times (- 2)}$

$\displaystyle \sf = \bigg \{ {3}^{2} - {2}^{3} \bigg \} \div {4}^{2}$

$\displaystyle \sf = \frac{ {3}^{2} - {2}^{3} }{ {4}^{2} }$

$\displaystyle \sf = \frac{ 9 - 8 }{ 16}$

$\displaystyle \sf = \frac{ 1 }{ 16}$

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