Solve for x 256^-2=16^(3x-1)

$256^{- 2} = 16^{3 x - 1}$

Step 1

Rewrite the equation as $16^{3 x - 1} = 256^{- 2}$ .

$16^{3 x - 1} = 256^{- 2}$

Step 2

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

$4^{2 (3 x - 1)} = 4^{4 \cdot - 2}$

Step 3

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

$2 (3 x - 1) = 4 \cdot - 2$

Step 4

Solve for $x$ .

Multiply $4$ by $- 2$ .

$2 (3 x - 1) = - 8$

Divide each term in $2 (3 x - 1) = - 8$ by $2$ and simplify.

Divide each term in $2 (3 x - 1) = - 8$ by $2$ .

$\frac{2 (3 x - 1)}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (3 x - 1)}{2} = \frac{- 8}{2}$

Divide $3 x - 1$ by $1$ .

$3 x - 1 = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$3 x - 1 = - 4$

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

Add $1$ to both sides of the equation.

$3 x = - 4 + 1$

Add $- 4$ and $1$ .

$3 x = - 3$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $3$ .

$x = - 1$