Algebra Examples

$2^{x + 4} \cdot 2^{4 x + 6} = 2^{2 x + 1}$

Step 1

Multiply $2^{x + 4}$ by $2^{4 x + 6}$ 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.

$2^{x + 4 + 4 x + 6} = 2^{2 x + 1}$

Step 1.2

Add $x$ and $4 x$ .

$2^{5 x + 4 + 6} = 2^{2 x + 1}$

Step 1.3

Add $4$ and $6$ .

$2^{5 x + 10} = 2^{2 x + 1}$

Step 2

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

$5 x + 10 = 2 x + 1$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $2 x$ from both sides of the equation.

$5 x + 10 - 2 x = 1$

Step 3.1.2

Subtract $2 x$ from $5 x$ .

$3 x + 10 = 1$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $10$ from both sides of the equation.

$3 x = 1 - 10$

Step 3.2.2

Subtract $10$ from $1$ .

$3 x = - 9$

Step 3.3

Divide each term in $3 x = - 9$ by $3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $3 x = - 9$ by $3$ .

$\frac{3 x}{3} = \frac{- 9}{3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 9}{3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{3}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $- 9$ by $3$ .

$x = - 3$