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

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

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

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

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

$4^{- (x - 4)} = 16^{- 1}$

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

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

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

$- (x - 4) = - 2$

Solve for $x$ .

Simplify $- (x - 4)$ .

Apply the distributive property.

$- x - - 4 = - 2$

Multiply $- 1$ by $- 4$ .

$- x + 4 = - 2$

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- x = - 2 - 4$

Subtract $4$ from $- 2$ .

$- x = - 6$

Divide each term in $- x = - 6$ by $- 1$ and simplify.

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x = 6$