Finite Math Examples

$3^{8 x} \cdot 3^{4 x} = 729$

Step 1

Multiply $3^{8 x}$ by $3^{4 x}$ by adding the exponents.

Tap for more steps...

Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3^{8 x + 4 x} = 729$

Step 1.2

Add $8 x$ and $4 x$ .

$3^{12 x} = 729$

Step 2

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

$3^{12 x} = 3^{6}$

Step 3

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

$12 x = 6$

Step 4

Divide each term in $12 x = 6$ by $12$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $12 x = 6$ by $12$ .

$\frac{12 x}{12} = \frac{6}{12}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $12$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{6}{12}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{12}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Cancel the common factor of $6$ and $12$ .

Tap for more steps...

Step 4.3.1.1

Factor $6$ out of $6$ .

$x = \frac{6 (1)}{12}$

Step 4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.3.1.2.1

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$