Solve for x (4^3)/(4^(2x))=4^(x+3)

$\frac{4^{3}}{4^{2 x}} = 4^{x + 3}$

Move $4^{2 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{3} \cdot 4^{- 2 x} = 4^{x + 3}$

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

$4^{3 - 2 x} = 4^{x + 3}$

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

$3 - 2 x = x + 3$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 - 2 x - x = 3$

Subtract $x$ from $- 2 x$ .

$3 - 3 x = 3$

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

Subtract $3$ from both sides of the equation.

$- 3 x = 3 - 3$

Subtract $3$ from $3$ .

$- 3 x = 0$

Divide each term in $- 3 x = 0$ by $- 3$ and simplify.

Divide each term in $- 3 x = 0$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Divide $x$ by $1$ .

$x = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$x = 0$