Trigonometry Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Combine the numerators over the common denominator.

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

Step 2.1.4

Add $1$ and $1$ .

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

Step 2.2

Multiply $2$ by $3$ .

$6 n^{\frac{2}{3}} + 2 \cdot - 4 n^{\frac{1}{3}} n^{\frac{4}{3}}$

Step 2.3

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

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Step 2.3.1

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

$6 n^{\frac{2}{3}} + 2 \cdot - 4 (n^{\frac{4}{3}} n^{\frac{1}{3}})$

Step 2.3.2

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

$6 n^{\frac{2}{3}} + 2 \cdot - 4 n^{\frac{4}{3} + \frac{1}{3}}$

Step 2.3.3

Combine the numerators over the common denominator.

$6 n^{\frac{2}{3}} + 2 \cdot - 4 n^{\frac{4 + 1}{3}}$

Step 2.3.4

Add $4$ and $1$ .

$6 n^{\frac{2}{3}} + 2 \cdot - 4 n^{\frac{5}{3}}$

Step 2.4

Multiply $2$ by $- 4$ .

$6 n^{\frac{2}{3}} - 8 n^{\frac{5}{3}}$