Question

By what number should (-3/2)-² be divided so that the quotient is (9/2)-²​

Answer 1

$\huge\color{aqua}answer : -$

-->9

$\huge\color{violet}explanation:-$

☆To find:-

• The number by which (-3/2)-² should be divided so that the quotient is

(9/2)-²

☆Formula:-

• Dividend= Divisor ×Quotient +Remainder

☆Given:-

• Dividend = (-3/2)-²

• Quotient = (9/2)-²

• Remainder= 0

☆Assuming:-

• Let tye number ( Divisor) be x

☆Solution:-

ATQ

$( \frac{ - 3}{2} ) ^{ - 2} = x \times (\frac{9}{2} ) ^{ - 2} + 0 \\ = >( \frac{ - 2}{3} ) ^{2} = x \times( \frac{2}{9})^{2} \\ = > \frac{4}{9} =x \frac{4}{81} = \frac{4x}{81} \\ = > 4 \times 81 = 4x \times 9 \\ = > 324 = 36x \\ = > x = \frac{324}{36} = \frac{54}{6} =9$

☆Hence:-

• The number by which (-3/2)-² should be divided so that the quotient is (9/2)-² is 9

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☆Verification:-

LHS:

$( { \frac{ - 3}{2}) }^{ - 2} \div 9 \\ = > {( \frac{ - 2}{3} )}^{2} \times \frac{1}{9} \\ = > \frac{4}{9} \times \frac{1}{9} = \frac{4}{81}$

RHS

${( \frac{9}{2} )}^{ - 2} \\ = > ( \frac{2}{9} ) ^{2} \\ = > \frac{4}{81}$

• Therefore,LHS = RHS

• Hence, verified

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hope it helps :)