Solve for x 2^x=1/16

$2^{x} = \frac{1}{16}$

Raise $16$ to the power of $1$ .

$2^{x} = \frac{1}{16^{1}}$

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x} = 16^{- 1}$

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

$2^{x} = 2^{- 4}$

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

$x = - 4$