Solve for x 64^(2x-11)=(1/16)^(-x+11)

$64^{2 x - 11} = {(\frac{1}{16})}^{- x + 11}$

Apply the product rule to $\frac{1}{16}$ .

$64^{2 x - 11} = \frac{1^{- x + 11}}{16^{- x + 11}}$

One to any power is one.

$64^{2 x - 11} = \frac{1}{16^{- x + 11}}$

Move $16^{- x + 11}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$64^{2 x - 11} = 16^{- (- x + 11)}$

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

$4^{3 (2 x - 11)} = 4^{2 (- (- x + 11))}$

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

$3 (2 x - 11) = 2 (- (- x + 11))$

Solve for $x$ .

Simplify $3 (2 x - 11)$ .

Start simplifying.

$0 + 0 + 3 (2 x - 11) = 2 (- (- x + 11))$

Simplify by adding zeros.

$3 (2 x - 11) = 2 (- (- x + 11))$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 11 = 2 (- (- x + 11))$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 11 = 2 (- (- x + 11))$

Multiply $3$ by $- 11$ .

$6 x - 33 = 2 (- (- x + 11))$

Simplify $2 (- (- x + 11))$ .

Apply the distributive property.

$6 x - 33 = 2 (- - x - 1 \cdot 11)$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$6 x - 33 = 2 (1 x - 1 \cdot 11)$

Multiply $x$ by $1$ .

$6 x - 33 = 2 (x - 1 \cdot 11)$

Multiply $- 1$ by $11$ .

$6 x - 33 = 2 (x - 11)$

Apply the distributive property.

$6 x - 33 = 2 x + 2 \cdot - 11$

Multiply $2$ by $- 11$ .

$6 x - 33 = 2 x - 22$

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

Subtract $2 x$ from both sides of the equation.

$6 x - 33 - 2 x = - 22$

Subtract $2 x$ from $6 x$ .

$4 x - 33 = - 22$

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

Add $33$ to both sides of the equation.

$4 x = - 22 + 33$

Add $- 22$ and $33$ .

$4 x = 11$

Divide each term in $4 x = 11$ by $4$ and simplify.

Divide each term in $4 x = 11$ by $4$ .

$\frac{4 x}{4} = \frac{11}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{11}{4}$

Divide $x$ by $1$ .

$x = \frac{11}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{4}$

Decimal Form:

$x = 2.75$

Mixed Number Form:

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

Solve for x 64^(2x-11)=(1/16)^(-x+11)

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