Finite Math Examples

$p^{\frac{2}{3}} (2 p^{\frac{1}{3}} + 5 p)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$p^{\frac{2}{3}} (2 p^{\frac{1}{3}}) + p^{\frac{2}{3}} (5 p)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 p^{\frac{2}{3}} p^{\frac{1}{3}} + p^{\frac{2}{3}} (5 p)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$2 p^{\frac{2}{3}} p^{\frac{1}{3}} + 5 p^{\frac{2}{3}} p$

Step 2

Simplify each term.

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Step 2.1

Multiply $p^{\frac{2}{3}}$ by $p^{\frac{1}{3}}$ by adding the exponents.

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Step 2.1.1

Move $p^{\frac{1}{3}}$ .

$2 (p^{\frac{1}{3}} p^{\frac{2}{3}}) + 5 p^{\frac{2}{3}} p$

Step 2.1.2

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

$2 p^{\frac{1}{3} + \frac{2}{3}} + 5 p^{\frac{2}{3}} p$

Step 2.1.3

Combine the numerators over the common denominator.

$2 p^{\frac{1 + 2}{3}} + 5 p^{\frac{2}{3}} p$

Step 2.1.4

Add $1$ and $2$ .

$2 p^{\frac{3}{3}} + 5 p^{\frac{2}{3}} p$

Step 2.1.5

Divide $3$ by $3$ .

$2 p^{1} + 5 p^{\frac{2}{3}} p$

Step 2.2

Simplify $2 p^{1}$ .

$2 p + 5 p^{\frac{2}{3}} p$

Step 2.3

Multiply $p^{\frac{2}{3}}$ by $p$ by adding the exponents.

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Step 2.3.1

Move $p$ .

$2 p + 5 (p \cdot p^{\frac{2}{3}})$

Step 2.3.2

Multiply $p$ by $p^{\frac{2}{3}}$ .

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Step 2.3.2.1

Raise $p$ to the power of $1$ .

$2 p + 5 (p^{1} p^{\frac{2}{3}})$

Step 2.3.2.2

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

$2 p + 5 p^{1 + \frac{2}{3}}$

Step 2.3.3

Write $1$ as a fraction with a common denominator.

$2 p + 5 p^{\frac{3}{3} + \frac{2}{3}}$

Step 2.3.4

Combine the numerators over the common denominator.

$2 p + 5 p^{\frac{3 + 2}{3}}$

Step 2.3.5

Add $3$ and $2$ .

$2 p + 5 p^{\frac{5}{3}}$