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