Algebra Examples

$\frac{x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}}}{x^{\frac{3}{4}}}$

Step 1

Move $x^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}} x^{- \frac{3}{4}}$

Step 2

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{3}{4}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{3}{4}}$ .

$x^{- \frac{3}{4}} x^{\frac{5}{4}} {(x^{4})}^{\frac{1}{8}}$

Step 2.2

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

$x^{- \frac{3}{4} + \frac{5}{4}} {(x^{4})}^{\frac{1}{8}}$

Step 2.3

Combine the numerators over the common denominator.

$x^{\frac{- 3 + 5}{4}} {(x^{4})}^{\frac{1}{8}}$

Step 2.4

Add $- 3$ and $5$ .

$x^{\frac{2}{4}} {(x^{4})}^{\frac{1}{8}}$

Step 2.5

Cancel the common factor of $2$ and $4$ .

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Step 2.5.1

Factor $2$ out of $2$ .

$x^{\frac{2 (1)}{4}} {(x^{4})}^{\frac{1}{8}}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $4$ .

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{4})}^{\frac{1}{8}}$

Step 2.5.2.2

Cancel the common factor.

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{4})}^{\frac{1}{8}}$

Step 2.5.2.3

Rewrite the expression.

$x^{\frac{1}{2}} {(x^{4})}^{\frac{1}{8}}$

Step 3

Multiply the exponents in ${(x^{4})}^{\frac{1}{8}}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2}} x^{4 (\frac{1}{8})}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $8$ .

$x^{\frac{1}{2}} x^{4 \frac{1}{4 (2)}}$

Step 3.2.2

Cancel the common factor.

$x^{\frac{1}{2}} x^{4 \frac{1}{4 \cdot 2}}$

Step 3.2.3

Rewrite the expression.

$x^{\frac{1}{2}} x^{\frac{1}{2}}$

Step 4

Multiply $x^{\frac{1}{2}}$ by $x^{\frac{1}{2}}$ 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.

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 4.3

Add $1$ and $1$ .

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

Step 4.4

Divide $2$ by $2$ .

$x^{1}$

Step 5

Simplify $x^{1}$ .

$x$