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:
---> (a⁻¹ = 1/a)
---> ((a/b)ⁿ = (aⁿ)/(bⁿ))

and
(7/3) −¹ = 3/7. ---> (a⁻¹ = 1/a)
We have to find a number x such that

Multiplying both sides by 25/9, we get:

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