Question

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

Answer 1

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.