# By What Number Should ( 5 3 ) − 2 Be Multiplied So that the Product May Be ( 7 3 ) − 1 ? - Mathematics

Sum

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

#### 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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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 2 Powers
Exercise 2.2 | Q 11 | Page 19