Evaluate 16^(2p)=32^(p+3)

$16^{2 p} = 32^{p + 3}$

Step 1

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

$2^{4 (2 p)} = 2^{5 (p + 3)}$

Step 2

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

$4 (2 p) = 5 (p + 3)$

Step 3

Solve for $p$ .

Multiply $2$ by $4$ .

$8 p = 5 (p + 3)$

Simplify $5 (p + 3)$ .

Apply the distributive property.

$8 p = 5 p + 5 \cdot 3$

Multiply $5$ by $3$ .

$8 p = 5 p + 15$

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

Subtract $5 p$ from both sides of the equation.

$8 p - 5 p = 15$

Subtract $5 p$ from $8 p$ .

$3 p = 15$

Divide each term in $3 p = 15$ by $3$ and simplify.

Divide each term in $3 p = 15$ by $3$ .

$\frac{3 p}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 p}{3} = \frac{15}{3}$

Divide $p$ by $1$ .

$p = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$p = 5$