Solve for x 4^(-2x)*4^x=64

$4^{- 2 x} \cdot 4^{x} = 64$

Multiply $4^{- 2 x}$ by $4^{x}$ by adding the exponents.

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

$4^{- 2 x + x} = 64$

Add $- 2 x$ and $x$ .

$4^{- x} = 64$

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

$4^{- x} = 4^{3}$

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

$- x = 3$

Divide each term in $- x = 3$ by $- 1$ and simplify.

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$x = - 3$