Question

(2/3)^-2÷(3/2)^-2 choose the correct answer
( a) 16/81
(b) 4/9
(c) 9/4
(d) 81/16​

Answer 1

• Option (d) is Correct Answer.

$\Huge \mathbb{EXPLANATION ↓}$

We know,

• On removing (-) from indices, the number {with exponent} reciprocates itself i.e. $\rm {x}^{(-2)} = \frac{1}{{x}^{2}}$ .

Also,

• $\rm {x}^{n} \div {x}^{m} = {x}^{( n- m)}$

Now,

$\bf \large \: \: { \bigg( \frac{2}{3} \bigg)}^{ - 2} \div {\bigg( \frac{3}{2} \bigg)}^{ - 2} \\ \\ \to { \bigg( \frac{2}{3} \bigg)}^{ - 2} \div { \bigg( \frac{2}{3} \bigg)}^{2} \\ \\ \to {\bigg( \frac{2}{3} \bigg)}^{ - 2 - 2} = {\bigg( \frac{2}{3} \bigg)}^{ - 4} \\ \\ \to {\bigg( \frac{3}{2} \bigg)}^{4} \: \: = \frac{ {3}^{4} }{ {2}^{4} } \: \: = \red{ \frac{81}{16} }$

Hence,

• (2/3)^[-2] ÷ (3/2)^[-2] = 81/16