Question

If (1/5)^x = (125)^4, then the value of x.

Answer 1

x = - 12

Explanation:

using the rules of exponents

•
`(1)/(a)` =
`a^(-1)`

•
`(a^m)^(n)` =
`a^(mn)`

given

`((1)/(5)) ^(x)` =
`(125)^(4)`

`(5^(-1)) ^(x)` =
`(5^(3)) ^(4)`

`5^(-x)` =
`5^(3(4))` =
`5^(12)`

since the bases on both sides are equal, both 5 , then equate the exponents

- x = 12 ( multiply both sides by - 1 )

x = - 12