Question

If 16^x = 1/64, find the value of x.

Answer 1

x = -
`(3)/(2)`

Explanation:

`16^(x)` =
`(1)/(64)`

Raise 64 to the power of 1.

`16^(x)` =
`(1)/(64^(1) )`

Move
`64^(1)` to the numerator using the negative exponent rule.

`16^(x)` =
`64^(-1)`

Create equivalent expressions in the equation that all have equal bases.

`4^(2x)` =
`4^(-3)`

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

2x = -3

x = -
`(3)/(2)`