Basic Math Examples

$p^{\frac{11}{5}} (3 p^{\frac{4}{5}} + 9 p^{\frac{19}{5}})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$p^{\frac{11}{5}} (3 p^{\frac{4}{5}}) + p^{\frac{11}{5}} (9 p^{\frac{19}{5}})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 p^{\frac{11}{5}} p^{\frac{4}{5}} + p^{\frac{11}{5}} (9 p^{\frac{19}{5}})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$3 p^{\frac{11}{5}} p^{\frac{4}{5}} + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2

Simplify each term.

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Step 2.1

Multiply $p^{\frac{11}{5}}$ by $p^{\frac{4}{5}}$ by adding the exponents.

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Step 2.1.1

Move $p^{\frac{4}{5}}$ .

$3 (p^{\frac{4}{5}} p^{\frac{11}{5}}) + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2.1.2

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

$3 p^{\frac{4}{5} + \frac{11}{5}} + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2.1.3

Combine the numerators over the common denominator.

$3 p^{\frac{4 + 11}{5}} + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2.1.4

Add $4$ and $11$ .

$3 p^{\frac{15}{5}} + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2.1.5

Divide $15$ by $5$ .

$3 p^{3} + 9 p^{\frac{11}{5}} p^{\frac{19}{5}}$

Step 2.2

Multiply $p^{\frac{11}{5}}$ by $p^{\frac{19}{5}}$ by adding the exponents.

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Step 2.2.1

Move $p^{\frac{19}{5}}$ .

$3 p^{3} + 9 (p^{\frac{19}{5}} p^{\frac{11}{5}})$

Step 2.2.2

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

$3 p^{3} + 9 p^{\frac{19}{5} + \frac{11}{5}}$

Step 2.2.3

Combine the numerators over the common denominator.

$3 p^{3} + 9 p^{\frac{19 + 11}{5}}$

Step 2.2.4

Add $19$ and $11$ .

$3 p^{3} + 9 p^{\frac{30}{5}}$

Step 2.2.5

Divide $30$ by $5$ .

$3 p^{3} + 9 p^{6}$