Solve for x (1/128)^(-5x+8)=32^(-x+3)

${(\frac{1}{128})}^{- 5 x + 8} = 32^{- x + 3}$

Apply the product rule to $\frac{1}{128}$ .

$\frac{1^{- 5 x + 8}}{128^{- 5 x + 8}} = 32^{- x + 3}$

One to any power is one.

$\frac{1}{128^{- 5 x + 8}} = 32^{- x + 3}$

Move $128^{- 5 x + 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$128^{- (- 5 x + 8)} = 32^{- x + 3}$

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

$2^{7 (- (- 5 x + 8))} = 2^{5 (- x + 3)}$

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

$7 (- (- 5 x + 8)) = 5 (- x + 3)$

Solve for $x$ .

Simplify $7 (- (- 5 x + 8))$ .

Start simplifying.

$0 + 0 + 7 (- (- 5 x + 8)) = 5 (- x + 3)$

Simplify by adding zeros.

$7 (- (- 5 x + 8)) = 5 (- x + 3)$

Apply the distributive property.

$7 (- (- 5 x) - 1 \cdot 8) = 5 (- x + 3)$

Multiply.

Multiply $- 5$ by $- 1$ .

$7 (5 x - 1 \cdot 8) = 5 (- x + 3)$

Multiply $- 1$ by $8$ .

$7 (5 x - 8) = 5 (- x + 3)$

Apply the distributive property.

$7 (5 x) + 7 \cdot - 8 = 5 (- x + 3)$

Multiply.

Multiply $5$ by $7$ .

$35 x + 7 \cdot - 8 = 5 (- x + 3)$

Multiply $7$ by $- 8$ .

$35 x - 56 = 5 (- x + 3)$

Simplify $5 (- x + 3)$ .

Apply the distributive property.

$35 x - 56 = 5 (- x) + 5 \cdot 3$

Multiply.

Multiply $- 1$ by $5$ .

$35 x - 56 = - 5 x + 5 \cdot 3$

Multiply $5$ by $3$ .

$35 x - 56 = - 5 x + 15$

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

Add $5 x$ to both sides of the equation.

$35 x - 56 + 5 x = 15$

Add $35 x$ and $5 x$ .

$40 x - 56 = 15$

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

Add $56$ to both sides of the equation.

$40 x = 15 + 56$

Add $15$ and $56$ .

$40 x = 71$

Divide each term in $40 x = 71$ by $40$ and simplify.

Divide each term in $40 x = 71$ by $40$ .

$\frac{40 x}{40} = \frac{71}{40}$

Simplify the left side.

Cancel the common factor of $40$ .

Cancel the common factor.

$\frac{40 x}{40} = \frac{71}{40}$

Divide $x$ by $1$ .

$x = \frac{71}{40}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{71}{40}$

Decimal Form:

$x = 1.775$

Mixed Number Form:

$x = 1 \frac{31}{40}$

Solve for x (1/128)^(-5x+8)=32^(-x+3)

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