Solve for x (2^5)/(2^(-2x))=2^8

$\frac{2^{5}}{2^{- 2 x}} = 2^{8}$

Move $2^{- 2 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{5} \cdot 2^{2 x} = 2^{8}$

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

$2^{5 + 2 x} = 2^{8}$

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

$5 + 2 x = 8$

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$2 x = 8 - 5$

Subtract $5$ from $8$ .

$2 x = 3$

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 $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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