Algebra Examples

2 x^{\frac{2}{3}} \cdot x^{3}

$2 x^{\frac{2}{3}} \cdot x^{3}$

Step 1

Move

x^{3}

$x^{3}$ .

2 (x^{3} x^{\frac{2}{3}})

$2 (x^{3} x^{\frac{2}{3}})$

Step 2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

2 x^{3 + \frac{2}{3}}

$2 x^{3 + \frac{2}{3}}$

Step 3

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

2 x^{3 \cdot \frac{3}{3} + \frac{2}{3}}

$2 x^{3 \cdot \frac{3}{3} + \frac{2}{3}}$

Step 4

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

2 x^{\frac{3 \cdot 3}{3} + \frac{2}{3}}

$2 x^{\frac{3 \cdot 3}{3} + \frac{2}{3}}$

Step 5

Combine the numerators over the common denominator.

2 x^{\frac{3 \cdot 3 + 2}{3}}

$2 x^{\frac{3 \cdot 3 + 2}{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

3

$3$ by

3

$3$ .

2 x^{\frac{9 + 2}{3}}

$2 x^{\frac{9 + 2}{3}}$

Step 6.2

Add

9

$9$ and

2

$2$ .

2 x^{\frac{11}{3}}

$2 x^{\frac{11}{3}}$

2 x^{\frac{11}{3}}

$2 x^{\frac{11}{3}}$