Algebra Examples

$\frac{x \cdot x^{\frac{2}{5}}}{x^{- 3}}$

Step 1

Multiply $x$ by $x^{\frac{2}{5}}$ by adding the exponents.

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Step 1.1

Multiply $x$ by $x^{\frac{2}{5}}$ .

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Step 1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} \cdot x^{\frac{2}{5}}}{x^{- 3}}$

Step 1.1.2

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

$\frac{x^{1 + \frac{2}{5}}}{x^{- 3}}$

Step 1.2

Write $1$ as a fraction with a common denominator.

$\frac{x^{\frac{5}{5} + \frac{2}{5}}}{x^{- 3}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x^{\frac{5 + 2}{5}}}{x^{- 3}}$

Step 1.4

Add $5$ and $2$ .

$\frac{x^{\frac{7}{5}}}{x^{- 3}}$

Step 2

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{\frac{7}{5}} x^{3}$

Step 3

Multiply $x^{\frac{7}{5}}$ by $x^{3}$ by adding the exponents.

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Step 3.1

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

$x^{\frac{7}{5} + 3}$

Step 3.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x^{\frac{7}{5} + 3 \cdot \frac{5}{5}}$

Step 3.3

Combine $3$ and $\frac{5}{5}$ .

$x^{\frac{7}{5} + \frac{3 \cdot 5}{5}}$

Step 3.4

Combine the numerators over the common denominator.

$x^{\frac{7 + 3 \cdot 5}{5}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $5$ .

$x^{\frac{7 + 15}{5}}$

Step 3.5.2

Add $7$ and $15$ .

$x^{\frac{22}{5}}$