Question

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

Answer 1

`\displaystyle x^(-1)=(1)/(25)`

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)=(1)/(x)=((1)/(4)^2)/((4)/(5)^(-2))`

Operating:

`\displaystyle x^(-1)=(1)/(4)^2*(5)/(4)^(-2)`

`\displaystyle x^(-1)=(1)/(16)*(16)/(25)`

`\mathbf{\displaystyle x^(-1)=(1)/(25)}`