Solve for x (1/4)^x=16

${(\frac{1}{4})}^{x} = 16$

Step 1

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{x}}{4^{x}} = 16$

Step 2

One to any power is one.

$\frac{1}{4^{x}} = 16$

Step 3

Move $4^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{- x} = 16$

Step 4

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

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

Step 5

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

$- x = 2$

Step 6

Divide each term in $- x = 2$ by $- 1$ and simplify.

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$