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If X = ( 4 5 ) − 2 ÷ ( 1 4 ) 2 , Find the Value of X−1. - Mathematics

Sum

If \[x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2\], find the value of x−1.

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Solution

 First, we have to find x.
\[x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2\]   →((a/b)n = (an)/(bn))
`=(4^(-2)/5^(-2))xx4^2`

`=4^0/5^(-2)`

`=1/56(-2)`  → (a0 = 1)

Hence, the value of x−1 is:

`x^(-1)=(1/5^(-2))^(-1)`

`=(5^2)^(-1)`    →(a−1 = 1/a)

`=1/5^2`      →(a−1 = 1/a)

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 2 Powers
Exercise 2.2 | Q 13.2 | Page 19
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