Solve for w 2^(w+4)*2^(4w+6)=2^(2w+1)

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

Step 1

Multiply $2^{w + 4}$ by $2^{4 w + 6}$ by adding the exponents.

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

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

Add $w$ and $4 w$ .

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

Add $4$ and $6$ .

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

Step 2

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

$5 w + 10 = 2 w + 1$

Step 3

Solve for $w$ .

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

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

$5 w + 10 - 2 w = 1$

Subtract $2 w$ from $5 w$ .

$3 w + 10 = 1$

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

Subtract $10$ from both sides of the equation.

$3 w = 1 - 10$

Subtract $10$ from $1$ .

$3 w = - 9$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $w$ by $1$ .

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

Simplify the right side.

Divide $- 9$ by $3$ .

$w = - 3$