Answer:
[tex]\displaystyle x^{-1}=\frac{1}{25}[/tex]
Step-by-step explanation:
We are given the value of x:
[tex]x= (4/5)^{-2}[/tex] divided by [tex](1/4)^2[/tex]
We need to find the reciprocal of x or:
[tex]\displaystyle x^{-1}=\frac{1}{x}=\frac{\frac{1}{4}^2}{\frac{4}{5}^{-2}}[/tex]
Operating:
[tex]\displaystyle x^{-1}=\frac{1}{4}^2*\frac{5}{4}^{-2}[/tex]
[tex]\displaystyle x^{-1}=\frac{1}{16}*\frac{16}{25}[/tex]
[tex]\mathbf{\displaystyle x^{-1}=\frac{1}{25}}[/tex]
