Evaluate 3^(4x-9)=1/243

$3^{4 x - 9} = \frac{1}{243}$

Step 1

Raise $243$ to the power of $1$ .

$3^{4 x - 9} = \frac{1}{243^{1}}$

Step 2

Move $243^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{4 x - 9} = 243^{- 1}$

Step 3

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

$3^{4 x - 9} = 3^{- 5}$

Step 4

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

$4 x - 9 = - 5$

Step 5

Solve for $x$ .

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

Add $9$ to both sides of the equation.

$4 x = - 5 + 9$

Add $- 5$ and $9$ .

$4 x = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$