Question

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

Answer 1

 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)