Solve for n 2^(-2n)=2^6

$2^{- 2 n} = 2^{6}$

Step 1

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

$2^{- 2 n} = 2^{6}$

Step 2

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

$- 2 n = 6$

Step 3

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

Divide each term in $- 2 n = 6$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{6}{- 2}$

Divide $n$ by $1$ .

$n = \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$n = - 3$