By what number should $(\frac{5}{3})^{-2}$ be multiplied so that the product may be $(\frac{7}{3})^{-1}$?

To do:  

We have to find the number that should be multiplied by $(\frac{5}{3})^{-2}$ so that the product is equal to $(\frac{7}{3})^{-1}$.

Solution:

Let the number that should be multiplied by $(\frac{5}{3})^{-2}$ so that the product is equal to $(\frac{7}{3})^{-1}$ be $x$.

Therefore,

$(\frac{5}{3})^{-2}\times x=(\frac{7}{3})^{-1}$

$(\frac{3}{5})^2\times x=(\frac{3}{7})^1$

$x=\frac{3\times5^2}{7\times3^2}$

$x=\frac{25}{21}$

Hence, the number that should be multiplied by $(\frac{5}{3})^{-2}$ so that the product is equal to $(\frac{7}{3})^{-1}$ is $\frac{25}{21}$.  

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Updated on: 10-Oct-2022

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