By what number should


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


Expressing as a positive exponent, we have:

$\left(\frac{5}{3}\right)^{-2}=\frac{1}{(5 / 3)^{2}} \quad \cdots\left(a^{-1}=1 / a\right)$

$=\frac{1}{25 / 9} \quad \ldots>\left((a / b)^{n}=\left(a^{n}\right) /\left(b^{n}\right)\right)$



(7/3)1 = 3/7.                ---> (a−1 = 1/a)

We have to find a number x such that

$\frac{9}{25} \times x=\frac{3}{7}$

Multiplying both sides by 25/9, we get:

$x=\frac{3}{7} \times \frac{25}{9}=\frac{1}{7} \times \frac{25}{3}=\frac{25}{21}$

Hence, (5/3)−2 should be multiplied by 25/21 to obtain (7/3)−1.

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