Question

if x= (4/5)^-2 divided by (1/4)^2,find the value of x^-1

Answer 1

Answer:

$\displaystyle x^{-1}=\frac{1}{25}$

Step-by-step explanation:

We are given the value of x:

$x= (4/5)^{-2}$ divided by $(1/4)^2$

We need to find the reciprocal of x or:

$\displaystyle x^{-1}=\frac{1}{x}=\frac{\frac{1}{4}^2}{\frac{4}{5}^{-2}}$

Operating:

$\displaystyle x^{-1}=\frac{1}{4}^2*\frac{5}{4}^{-2}$

$\displaystyle x^{-1}=\frac{1}{16}*\frac{16}{25}$

$\mathbf{\displaystyle x^{-1}=\frac{1}{25}}$