Solve for x 16^(-x)=1/64

$16^{- x} = \frac{1}{64}$

Step 1

Raise $64$ to the power of $1$ .

$16^{- x} = \frac{1}{64^{1}}$

Step 2

Move $64^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$16^{- x} = 64^{- 1}$

Step 3

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

$4^{2 (- x)} = 4^{- 3}$

Step 4

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

$2 (- x) = - 3$

Step 5

Solve for $x$ .

Multiply $- 1$ by $2$ .

$- 2 x = - 3$

Divide each term in $- 2 x = - 3$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 3$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 3}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

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