Solve for x 2^(-x)*2^(3x)=64

$2^{- x} \cdot 2^{3 x} = 64$

Multiply $2^{- x}$ by $2^{3 x}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{- x + 3 x} = 64$

Add $- x$ and $3 x$ .

$2^{2 x} = 64$

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

$2^{2 x} = 2^{6}$

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

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$