Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Add $- 3$ and $5$ .

$x^{\frac{2}{4}} {(x^{3})}^{\frac{3}{4}}$

Step 2.5

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

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Step 2.5.1

Factor $2$ out of $2$ .

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

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $4$ .

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{3})}^{\frac{3}{4}}$

Step 2.5.2.2

Cancel the common factor.

$x^{\frac{2 \cdot 1}{2 \cdot 2}} {(x^{3})}^{\frac{3}{4}}$

Step 2.5.2.3

Rewrite the expression.

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

Step 3

Multiply the exponents in ${(x^{3})}^{\frac{3}{4}}$ .

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Step 3.1

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

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

Step 3.2

Multiply $3 (\frac{3}{4})$ .

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Step 3.2.1

Combine $3$ and $\frac{3}{4}$ .

$x^{\frac{1}{2}} x^{\frac{3 \cdot 3}{4}}$

Step 3.2.2

Multiply $3$ by $3$ .

$x^{\frac{1}{2}} x^{\frac{9}{4}}$

Step 4

Multiply $x^{\frac{1}{2}}$ by $x^{\frac{9}{4}}$ 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.

$x^{\frac{1}{2} + \frac{9}{4}}$

Step 4.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{1}{2} \cdot \frac{2}{2} + \frac{9}{4}}$

Step 4.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

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

$x^{\frac{2}{2 \cdot 2} + \frac{9}{4}}$

Step 4.3.2

Multiply $2$ by $2$ .

$x^{\frac{2}{4} + \frac{9}{4}}$

Step 4.4

Combine the numerators over the common denominator.

$x^{\frac{2 + 9}{4}}$

Step 4.5

Add $2$ and $9$ .

$x^{\frac{11}{4}}$