Basic Math Examples

$p^{\frac{3}{4}} (p^{\frac{1}{4}} + 3 p^{\frac{9}{4}})$

Step 1

Apply the distributive property.

$p^{\frac{3}{4}} p^{\frac{1}{4}} + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 2

Multiply $p^{\frac{3}{4}}$ by $p^{\frac{1}{4}}$ by adding the exponents.

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Step 2.1

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

$p^{\frac{3}{4} + \frac{1}{4}} + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 2.2

Combine the numerators over the common denominator.

$p^{\frac{3 + 1}{4}} + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 2.3

Add $3$ and $1$ .

$p^{\frac{4}{4}} + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 2.4

Divide $4$ by $4$ .

$p^{1} + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 3

Simplify $p^{1}$ .

$p + p^{\frac{3}{4}} (3 p^{\frac{9}{4}})$

Step 4

Rewrite using the commutative property of multiplication.

$p + 3 p^{\frac{3}{4}} p^{\frac{9}{4}}$

Step 5

Multiply $p^{\frac{3}{4}}$ by $p^{\frac{9}{4}}$ by adding the exponents.

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Step 5.1

Move $p^{\frac{9}{4}}$ .

$p + 3 (p^{\frac{9}{4}} p^{\frac{3}{4}})$

Step 5.2

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

$p + 3 p^{\frac{9}{4} + \frac{3}{4}}$

Step 5.3

Combine the numerators over the common denominator.

$p + 3 p^{\frac{9 + 3}{4}}$

Step 5.4

Add $9$ and $3$ .

$p + 3 p^{\frac{12}{4}}$

Step 5.5

Divide $12$ by $4$ .

$p + 3 p^{3}$