Question

if 4 /5 to the power 13 ÷ 4 /5 to the power 19 = 5 /4 to the power x then the value of x is?

Answer 1

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Answer 2

Given,
$\frac{ { (\frac{4}{5}) }^{13} }{ { (\frac{4}{5}) }^{19} } = {( \frac{5}{4} )}^{x}$

As we know that,
${x}^{a} \div {x}^{b} = {x}^{ a-b }$
So,
$\frac{ { (\frac{4}{5}) }^{13} }{ { (\frac{4}{5}) }^{19} } = {( \frac{4}{5} )}^{13 - 19} = { (\frac{4}{5}) }^{ - 6} = { (\frac{5}{4} )}^{6}.$
As bases are same
Therefore
Exponents will also be same.
=>x = 6.

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