Question

by what number should (5/4)^-3 be divided so that the quotient may be (15/16)^-2

Answer 1

Let's assume the number as x

According to Question,

$\dfrac{\bigg( \dfrac{5}{4} \bigg)^{ - 3}}{x} = \bigg( \dfrac{15}{16} \bigg)^{ - 2} \\ \\ \implies \bigg( \dfrac{5}{4} \bigg) ^{ - 3} = \bigg( \dfrac{15}{16} \bigg) ^{ - 2} \times x \\ \\ \implies \bigg(\dfrac{4}{5} \bigg)^{3} = \bigg(\frac{16}{15} \bigg)^{2} \times x \\ \\ \implies \dfrac{(4)^{3} }{ {(5)}^{3} } = \dfrac{ {(16)}^{2} }{ {(15)}^{2} } \times x \\ \\ \implies \dfrac{64}{125} = \dfrac{256}{225} \times x \\ \\ \implies \dfrac{ \cancel{64} \: {}^{1} }{ \cancel{125} \: {}^{5} } \times \dfrac{ \cancel{225} \: {}^{9} }{ \cancel{256} \: {}^{4} } = x \\ \\ \implies \dfrac{1 \times 9}{5 \times 4} = x \\ \\ \implies \boxed{ \dfrac{9}{20} = x }\\ \\ \implies \: 0.45 \approx \: x$

Hence, the number is $\mathbf{\dfrac{9}{20}}$

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Answer 2

The required number is 9/20 .

Here we suppose that number= X .

And put that value in the place of that number.

Then we simplified the index of the other numbers into positive values.

Then we again simplified and get the value of x .

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