Question

Refer the attachment.
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Answer 1

$\large{\underline{\underline{ \bf{⎆Question:-}}}}$

$\tt{ If ({ \frac{3}{5} )}^{n} } ({ \frac{5}{3} })^{n} = \frac{625}{81} \: then \: find \: the \: value \: of \: {n}^{3}$

$\large{\underline{\underline{ \bf{☂ Solution:-}}}}$

$\longmapsto \tt{ ({ \frac{5}{3} )}^{ - n} } ({ \frac{5}{3} })^{3n} = \frac{625}{81}$

$\longmapsto \tt{ ({ \frac{5}{3} )}^{ 2 n} } = ({ \frac{5}{3} })^{4}$

✧Indices are equal , since bases are equal .

$\longmapsto\tt{2n=4}$

$\longmapsto\tt{n=2}$

$∴ \: \tt{ {n}^{3} = 8}$

• Hence the value of n³ = 8