Algebra Examples

$\frac{3^{3}}{3^{y}} = \frac{1}{9}$

Step 1

Cancel the common factor of $3^{3}$ and $3^{y}$ .

Tap for more steps...

Step 1.1

Factor $3^{y}$ out of $3^{3}$ .

$\frac{3^{y} \cdot 3^{3 - y}}{3^{y}} = \frac{1}{9}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Multiply by $1$ .

$\frac{3^{y} \cdot 3^{3 - y}}{3^{y} \cdot 1} = \frac{1}{9}$

Step 1.2.2

Cancel the common factor.

$\frac{3^{y} \cdot 3^{3 - y}}{3^{y} \cdot 1} = \frac{1}{9}$

Step 1.2.3

Rewrite the expression.

$\frac{3^{3 - y}}{1} = \frac{1}{9}$

Step 1.2.4

Divide $3^{3 - y}$ by $1$ .

$3^{3 - y} = \frac{1}{9}$

Step 2

Solve for $y$ .

Tap for more steps...

Step 2.1

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

$3^{3 - y} = \frac{1}{9^{1}}$

Step 2.2

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

$3^{3 - y} = 9^{- 1}$

Step 2.3

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

$3^{3 - y} = 3^{- 2}$

Step 2.4

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

$3 - y = - 2$

Step 2.5

Solve for $y$ .

Tap for more steps...

Step 2.5.1

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

Tap for more steps...

Step 2.5.1.1

Subtract $3$ from both sides of the equation.

$- y = - 2 - 3$

Step 2.5.1.2

Subtract $3$ from $- 2$ .

$- y = - 5$

Step 2.5.2

Divide each term in $- y = - 5$ by $- 1$ and simplify.

Tap for more steps...

Step 2.5.2.1

Divide each term in $- y = - 5$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 5}{- 1}$

Step 2.5.2.2

Simplify the left side.

Tap for more steps...

Step 2.5.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 5}{- 1}$

Step 2.5.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 5}{- 1}$

Step 2.5.2.3

Simplify the right side.

Tap for more steps...

Step 2.5.2.3.1

Divide $- 5$ by $- 1$ .

$y = 5$