Algebra Examples

$\frac{3^{x - 2}}{3^{4}} = \frac{1}{9}$

Step 1

Cancel the common factor of $3^{x - 2}$ and $3^{4}$ .

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Step 1.1

Factor $3^{4}$ out of $3^{x - 2}$ .

$\frac{3^{4} \cdot 3^{x - 6}}{3^{4}} = \frac{1}{9}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

$\frac{3^{4} \cdot 3^{x - 6}}{3^{4} \cdot 1} = \frac{1}{9}$

Step 1.2.2

Cancel the common factor.

$\frac{3^{4} \cdot 3^{x - 6}}{3^{4} \cdot 1} = \frac{1}{9}$

Step 1.2.3

Rewrite the expression.

$\frac{3^{x - 6}}{1} = \frac{1}{9}$

Step 1.2.4

Divide $3^{x - 6}$ by $1$ .

$3^{x - 6} = \frac{1}{9}$

Step 2

Solve for $x$ .

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Step 2.1

Raise $9$ to the power of $1$ .

$3^{x - 6} = \frac{1}{9^{1}}$

Step 2.2

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

$3^{x - 6} = 9^{- 1}$

Step 2.3

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

$3^{x - 6} = 3^{- 2}$

Step 2.4

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

$x - 6 = - 2$

Step 2.5

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

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Step 2.5.1

Add $6$ to both sides of the equation.

$x = - 2 + 6$

Step 2.5.2

Add $- 2$ and $6$ .

$x = 4$