Question

How do you answer this?

Answer 1

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

Explanation:

Using the rules of exponents

`(a^m)^(n)` =
`a^(mn)`

`a^(-m)` ⇔
`(1)/(a^m)`

Note that 16 = 4² and 64 = 4³ , then

`16^(x)` =
`(1)/(64)` , can be expressed as

`(4^2)^(x)` =
`(1)/(4^3)` , that is

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

Since the bases on both sides are equal, then equate the exponents

2x = - 3 ( divide both sides by 2 )

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

Answer 2

x= -3/2

Explanation:

((4)²)^x = 1/(4)³

4²^x = 4³

thus the powers are same then

2x =-3

x=-3/2