Question

Find the value of (8/125)^-2/3

Answer 1

6.25

Explanation:

Using the rules of exponents

`((a)/(b)) ^{-(m)/(n) }` =
`((b)/(a)) ^{(m)/(n) }`

`a^{(m)/(n) }` =
`(\sqrt[n]{a} )^m`

Given

`((8)/(125)) ^{-(2)/(3) }`

=
`((125)/(8)) ^{(2)/(3) }`

=
`(\sqrt[3]{125} )^2` ×
`\frac{1}{(\sqrt[3]{8})^2 }`

= 5² ×
`(1)/(2^2)`

= 25 ×
`(1)/(4)`

=
`(25)/(4)`

= 6.25