Solve for x 343^(4x+9)=(1/49)^(-3x+9)

$343^{4 x + 9} = {(\frac{1}{49})}^{- 3 x + 9}$

Apply the product rule to $\frac{1}{49}$ .

$343^{4 x + 9} = \frac{1^{- 3 x + 9}}{49^{- 3 x + 9}}$

One to any power is one.

$343^{4 x + 9} = \frac{1}{49^{- 3 x + 9}}$

Move $49^{- 3 x + 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$343^{4 x + 9} = 49^{- (- 3 x + 9)}$

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

$7^{3 (4 x + 9)} = 7^{2 (- (- 3 x + 9))}$

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

$3 (4 x + 9) = 2 (- (- 3 x + 9))$

Solve for $x$ .

Simplify $3 (4 x + 9)$ .

Start simplifying.

$0 + 0 + 3 (4 x + 9) = 2 (- (- 3 x + 9))$

Simplify by adding zeros.

$3 (4 x + 9) = 2 (- (- 3 x + 9))$

Apply the distributive property.

$3 (4 x) + 3 \cdot 9 = 2 (- (- 3 x + 9))$

Multiply.

Multiply $4$ by $3$ .

$12 x + 3 \cdot 9 = 2 (- (- 3 x + 9))$

Multiply $3$ by $9$ .

$12 x + 27 = 2 (- (- 3 x + 9))$

Simplify $2 (- (- 3 x + 9))$ .

Apply the distributive property.

$12 x + 27 = 2 (- (- 3 x) - 1 \cdot 9)$

Multiply.

Multiply $- 3$ by $- 1$ .

$12 x + 27 = 2 (3 x - 1 \cdot 9)$

Multiply $- 1$ by $9$ .

$12 x + 27 = 2 (3 x - 9)$

Apply the distributive property.

$12 x + 27 = 2 (3 x) + 2 \cdot - 9$

Multiply.

Multiply $3$ by $2$ .

$12 x + 27 = 6 x + 2 \cdot - 9$

Multiply $2$ by $- 9$ .

$12 x + 27 = 6 x - 18$

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

Subtract $6 x$ from both sides of the equation.

$12 x + 27 - 6 x = - 18$

Subtract $6 x$ from $12 x$ .

$6 x + 27 = - 18$

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

Subtract $27$ from both sides of the equation.

$6 x = - 18 - 27$

Subtract $27$ from $- 18$ .

$6 x = - 45$

Divide each term in $6 x = - 45$ by $6$ and simplify.

Divide each term in $6 x = - 45$ by $6$ .

$\frac{6 x}{6} = \frac{- 45}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 45}{6}$

Divide $x$ by $1$ .

$x = \frac{- 45}{6}$

Simplify the right side.

Cancel the common factor of $- 45$ and $6$ .

Factor $3$ out of $- 45$ .

$x = \frac{3 (- 15)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 15}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot - 15}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{- 15}{2}$

Move the negative in front of the fraction.

$x = - \frac{15}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{2}$

Decimal Form:

$x = - 7.5$

Mixed Number Form:

$x = - 7 \frac{1}{2}$

Solve for x 343^(4x+9)=(1/49)^(-3x+9)

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