Question

by what number should (3/5)^-2 be multiplied to get (3/2)^-2 ?​

Answer 1

Answer:

$\mathtt{LET:-}$

$\mathtt\blue{LET \: THE \: NUMBER \: BE \: X}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{USED \: FORMULA:-}$

$\mathtt \blue{ {a}^{ - m} = \frac{1}{ {a}^{m} } }$

$\mathtt\blue{(\frac{a}{b})^m = \frac{a^m}{b^m}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{ACCORDING \: TO \: QUES : - }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt\blue{THE \: EQUATION \: BECOMES \downarrow}$

$\implies \mathtt \blue{ (\frac{3}{5})^{ - 2} \times x =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{SOLUTION:-}$

$\implies \mathtt \blue{ (\frac{3}{5})^{ - 2} \times x =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\implies \mathtt \blue{ \frac{ {5}^{2} }{3^{2} } \times x = } \mathtt{ \frac{ {2}^{2} }{ {3}^{2} } }$

$\implies \mathtt \blue{ \frac{ 25}{9 } \times x = } \mathtt{ \frac{ 4 }{ 9 } }$

$\implies \mathtt \blue{x = } \mathtt{ \frac{ 4 }{ 9 } \times \frac{9}{25} }$

$\implies \mathtt \blue{x = } \mathtt{ \frac{ 4 }{ 25}}$

$\implies \mathtt \blue{x = } \mathtt{ \frac{ {2}^{2} }{ {5}^{2} }}$

$\implies \mathtt \blue{x = } \mathtt{ (\frac{ {2}}{ {5} } )^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{VERIFICATION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies \mathtt \blue{ (\frac{3}{5})^{ - 2} \times ( \frac{2}{5})^{2} =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\implies \mathtt \blue{ \frac{5 ^{2} }{3^{2}} \times \frac{2^{2} }{5^{2} } =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\implies \mathtt \blue{ \frac{ {2}^{2} }{ {3}^{2} } =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\implies \mathtt \blue{ \frac{ {3}^{ - 2} }{ {2}^{ - 2} } =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\implies \mathtt \blue{ ( \frac{ {3} }{ {2} })^{ - 2} =} \mathtt{ ( \frac{3}{2})^{ - 2} }$

$\mathtt\blue{ \: \: \: \: \: \: \: \: \: \: \: \: LHS \: \: \: = }\mathtt{RHS}$

$\mathtt\blue{ \: \: \: \: \: \: \: \: \: \: \: HENCE, VERIFIED}$