Sum

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

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#### Solution

Expressing as a positive exponent, we have:

`(5/3)^(-2)=1/(5/3)^2` → (a^{−1} = 1/a)

`=1/(25/9)` → ((a/b)^{n} = (a^{n})/(b^{n}))

and

(7/3)−^{1} = 3/7. → (a^{−1} = 1/a)

We have to find a number x such that

`9/25xx x=3/7`

Multiplying both sides by 25/9, we get:

`x=3/7xx25/9=1/7xx25/3=25/21`

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

Concept: Powers with Negative Exponents

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