Question

(3/2)^-3 को किस संख्या से भाग दिया जाए कि भागफल (4/9)^-2
प्राप्त हो?​

Answer 1

प्रश्न :- (3/2)^-3 को किस संख्या से भाग दिया जाए कि भागफल (4/9)^-2 प्राप्त हो ?

उतर :-

माना (3/2)^-3 को x से भाग देने पर भागफल (4/9)^-2 प्राप्त होता है l

तब,

→ (3/2)^(-3) ÷ x = (4/9)^(-2)

→ (3/2)^(-3) ÷ x = {(2/3)²}^(-2)

→ (3/2)^(-3) ÷ x = (2/3)^(2 * -2) { ∵ (a^b)^c = (a)^(b*c) } .

→ (3/2)^(-3) ÷ x = (2/3)^(-4)

→ (3/2)^(-3) ÷ x = 1 / (2/3)⁴ { ∵ a^(-b) = 1/a^b .}

→ (3/2)^(-3) ÷ x = (3/2)⁴

→ (3/2)^(-3) / x = (3/2)⁴

→ x = (3/2)^(-3) / (3/2)⁴

→ x = (3/2)^(-3) ÷ (3/2)⁴

{ ∵ a^b ÷ a^c = a^( b - c) } .

→ x = (3/2)^ (-3 - 4)

→ x = (3/2)^(-7)

→ x = 1/(3/2)^7

→ x = (2/3)⁷

अत, (3/2)^(-3) को (2/3)⁷ से भाग देने पर भागफल (4/9)^(-2) प्राप्त होगा l

Answer 2

Step-by-step explanation:

हल:- माना संख्या = a

$\bigg( \frac{3}{2} \bigg) ^{ - 3} \div \mathrm{ a } = \bigg( \frac{4}{9} \bigg) ^{ - 2}$

$⟹ \bigg( \frac{3}{2} \bigg) ^{ - 3} \times \frac{1}{ \mathrm{a}} = \bigg( \frac{4}{9} \bigg)^{ - 2}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{4}{9} \bigg)^{ - 2} \div \bigg( \frac{3}{2} \bigg)^{ - 3}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{9}{4} \bigg)^{2} \div \bigg( \frac{3}{2} \bigg)^{ - 3}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{3}{2} \bigg) ^{2 \times 2} \div \bigg( \frac{3}{2} \bigg) ^{ - 3}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{3}{2} \bigg) ^{4} \div \bigg( \frac{3}{2} \bigg)^{ - 3}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{3}{2} \bigg) ^{4 - ( - 3)}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{3}{2} \bigg)^{7}$

$⟹ \mathrm{ \frac{1}{a} } = \bigg( \frac{2}{3} \bigg)^{7}$

$\therefore \: \: \mathrm{ a} = \bigg( \frac{2}{3} \bigg)^{7}$