Algebra Examples

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

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 $P$ .

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Step 3.1

Multiply $2$ by $4$ .

$8 P = 5 (P + 3)$

Step 3.2

Simplify $5 (P + 3)$ .

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Multiply $5$ by $3$ .

$8 P = 5 P + 15$

Step 3.3

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

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Step 3.3.1

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

$8 P - 5 P = 15$

Step 3.3.2

Subtract $5 P$ from $8 P$ .

$3 P = 15$

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $3$ .

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Step 3.4.2.1.1

Cancel the common factor.

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

Step 3.4.2.1.2

Divide $P$ by $1$ .

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

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $15$ by $3$ .

$P = 5$