Algebra Examples

$\frac{x^{5} \cdot x^{\frac{4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1

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

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Step 1.1

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

$\frac{x^{5 + \frac{4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1.2

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

$\frac{x^{5 \cdot \frac{5}{5} + \frac{4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1.3

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

$\frac{x^{\frac{5 \cdot 5}{5} + \frac{4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x^{\frac{5 \cdot 5 + 4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $5$ .

$\frac{x^{\frac{25 + 4}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 1.5.2

Add $25$ and $4$ .

$\frac{x^{\frac{29}{5}}}{x^{\frac{2}{5}} \cdot x}$

Step 2

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

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Step 2.1

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

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Step 2.1.1

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

$\frac{x^{\frac{29}{5}}}{x^{\frac{2}{5}} \cdot x^{1}}$

Step 2.1.2

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

$\frac{x^{\frac{29}{5}}}{x^{\frac{2}{5} + 1}}$

Step 2.2

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

$\frac{x^{\frac{29}{5}}}{x^{\frac{2}{5} + \frac{5}{5}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{x^{\frac{29}{5}}}{x^{\frac{2 + 5}{5}}}$

Step 2.4

Add $2$ and $5$ .

$\frac{x^{\frac{29}{5}}}{x^{\frac{7}{5}}}$

Step 3

Move $x^{\frac{7}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{29}{5}} x^{- \frac{7}{5}}$

Step 4

Multiply $x^{\frac{29}{5}}$ by $x^{- \frac{7}{5}}$ by adding the exponents.

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Step 4.1

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

$x^{\frac{29}{5} - \frac{7}{5}}$

Step 4.2

Combine the numerators over the common denominator.

$x^{\frac{29 - 7}{5}}$

Step 4.3

Subtract $7$ from $29$ .

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