Precalculus Examples

$- c^{\frac{2}{3}} (c^{\frac{1}{3}} + 2 c^{\frac{4}{3}})$

Step 1

Apply the distributive property.

$- c^{\frac{2}{3}} c^{\frac{1}{3}} - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 2

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

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Step 2.1

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

$- (c^{\frac{1}{3}} c^{\frac{2}{3}}) - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 2.2

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

$- c^{\frac{1}{3} + \frac{2}{3}} - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 2.3

Combine the numerators over the common denominator.

$- c^{\frac{1 + 2}{3}} - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 2.4

Add $1$ and $2$ .

$- c^{\frac{3}{3}} - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 2.5

Divide $3$ by $3$ .

$- c^{1} - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 3

Simplify the expression.

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Step 3.1

Simplify $- c^{1}$ .

$- c - c^{\frac{2}{3}} (2 c^{\frac{4}{3}})$

Step 3.2

Rewrite using the commutative property of multiplication.

$- c - 1 \cdot 2 c^{\frac{2}{3}} c^{\frac{4}{3}}$

Step 4

Simplify each term.

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Step 4.1

Multiply $c^{\frac{2}{3}}$ by $c^{\frac{4}{3}}$ by adding the exponents.

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Step 4.1.1

Move $c^{\frac{4}{3}}$ .

$- c - 1 \cdot 2 (c^{\frac{4}{3}} c^{\frac{2}{3}})$

Step 4.1.2

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

$- c - 1 \cdot 2 c^{\frac{4}{3} + \frac{2}{3}}$

Step 4.1.3

Combine the numerators over the common denominator.

$- c - 1 \cdot 2 c^{\frac{4 + 2}{3}}$

Step 4.1.4

Add $4$ and $2$ .

$- c - 1 \cdot 2 c^{\frac{6}{3}}$

Step 4.1.5

Divide $6$ by $3$ .

$- c - 1 \cdot 2 c^{2}$

Step 4.2

Multiply $- 1$ by $2$ .

$- c - 2 c^{2}$