Solve for X 7^(-9X+1)=49^-12

$7^{- 9 X + 1} = 49^{- 12}$

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

$7^{- 9 X + 1} = 7^{2 \cdot - 12}$

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

$- 9 X + 1 = 2 \cdot - 12$

Solve for $X$ .

Multiply $2$ by $- 12$ .

$- 9 X + 1 = - 24$

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

Subtract $1$ from both sides of the equation.

$- 9 X = - 24 - 1$

Subtract $1$ from $- 24$ .

$- 9 X = - 25$

Divide each term in $- 9 X = - 25$ by $- 9$ and simplify.

Divide each term in $- 9 X = - 25$ by $- 9$ .

$\frac{- 9 X}{- 9} = \frac{- 25}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 X}{- 9} = \frac{- 25}{- 9}$

Divide $X$ by $1$ .

$X = \frac{- 25}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$X = \frac{25}{9}$

The result can be shown in multiple forms.

Exact Form:

$X = \frac{25}{9}$

Decimal Form:

$X = 2.\overline{7}$

Mixed Number Form:

$X = 2 \frac{7}{9}$