Question

If a/b= (3/5)³÷(3/5)², find the value of (a/b) ²​

Answer 1

$\huge\mathcal\pink{Given:}$

• $\sf{\frac{a}{b}}\:\sf{=}\:\sf{\frac{3}{5}}^³\:\sf{÷}\:\sf\frac{3}{5}^²$

$\huge\mathcal\pink{Find:}$

• $\sf{\frac{a}{b}}^²\:\sf{=\:?}$

$\huge\mathcal\pink{Solution:}$

${\:\::⟹\:}$$\sf\frac{a}{b}\:=\:\sf{\frac{3}{5}}^³\:÷\:\sf{\frac{3}{5}}^²$

${\:\::⟹\:}$$\sf{\frac{a}{b}}\:=$$\sf\frac{3\:༝\:3\:༝\:3}{5\:༝\:5\:༝\:5}\:÷\:\sf\frac{3\:༝\:3}{5\:༝\:5}$

${\:\::⟹\:}$$\sf{\frac{a}{b}}\:=$$\sf\frac{27}{125}\:÷\:\sf\frac{9}{25}$

${\:\::⟹\:}$$\sf{\frac{a}{b}}\:=$$\sf\frac{27}{125}\:༝\:\sf\frac{25}{9}$

${\:\::⟹\:}$$\sf{\frac{a}{b}}\:=$$\sf\frac{\cancel{27}^{\:3}}{\cancel{125}^{\:5}}\:༝\:\sf\frac{\cancel{25}}{\cancel{9}}$

${\:\::⟹\:}$$\sf{\frac{a}{b}}\:=$$\sf\frac{3}{5}$

• $\sf\small\red{Now,\:we\:find}\:\sf\small{\red{(\frac{a}{b})}^\red{²}}$

${\:\::⟹\:}$$\sf{(\frac{a}{b})^{²}}\:=$$\sf{(\frac{3}{5})}^²$

${\:\::⟹\:}$$\sf{(\frac{a}{b})^{²}}\:=$$\sf\frac{3\:༝\:3}{5\:༝\:5}$

${\:\::⟹\:}$$\sf{(\frac{a}{b})^{²}}\:=$$\sf\frac{9}{25}$

• $\small{\underline{\underline{\boxed{\sf{\bold{\green{So,\:the\:value\:of\:\:{(\frac{a}{b})}^2\:\:{is}\:\:{\frac{9}{25}}}}}}}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━$\small\purple{\sf{\bold{\sf{@ItsNothing}}}}$

Answer 2

Step-by-step explanation:

$\huge\sf\underline\green{answer}$

$\frac{a}{b} = ( \frac{3}{5} )^{3} \div ( \frac{3}{5} {})^{2}$

$\frac{a}{b} = \frac{3}{5}$

$( \frac{a}{b}) {}^{2} = \frac{9}{25}$