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