Question

(1/2)^x=16^2

Could you please help me with the step-by step? This problem is giving me trouble. ​

Answer 1

Write both sides as powers of 2. First,

1/2 = 2⁻¹

16 = 2⁴

so the equation can be rewritten as

(1/2)ˣ = 16²

(2⁻¹)ˣ = (2⁴)²

Recall that
`(a^b)^c=a^(bc)`, so that

2⁻ˣ = 2⁸

The bases are the same, so the exponents must be equal:

-x = 8

x = -8