Algebra Examples

$\frac{7 x^{- \frac{3}{4}} y^{\frac{5}{2}} z^{- \frac{2}{3}}}{56 x^{- \frac{1}{2}} y^{\frac{1}{4}}}$

Step 1

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

$\frac{7 y^{\frac{5}{2}} z^{- \frac{2}{3}}}{56 x^{- \frac{1}{2}} y^{\frac{1}{4}} x^{\frac{3}{4}}}$

Step 2

Move $z^{- \frac{2}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{7 y^{\frac{5}{2}}}{56 x^{- \frac{1}{2}} y^{\frac{1}{4}} x^{\frac{3}{4}} z^{\frac{2}{3}}}$

Step 3

Multiply $x^{- \frac{1}{2}}$ by $x^{\frac{3}{4}}$ by adding the exponents.

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Step 3.1

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

$\frac{7 y^{\frac{5}{2}}}{56 (x^{\frac{3}{4}} x^{- \frac{1}{2}}) y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.2

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

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{3}{4} - \frac{1}{2}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.3

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

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{3}{4} - \frac{1}{2} \cdot \frac{2}{2}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.4

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

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Step 3.4.1

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

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{3}{4} - \frac{2}{2 \cdot 2}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.4.2

Multiply $2$ by $2$ .

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{3}{4} - \frac{2}{4}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{3 - 2}{4}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 3.6

Subtract $2$ from $3$ .

$\frac{7 y^{\frac{5}{2}}}{56 x^{\frac{1}{4}} y^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 4

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

$\frac{7 y^{\frac{5}{2}} y^{- \frac{1}{4}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5

Multiply $y^{\frac{5}{2}}$ by $y^{- \frac{1}{4}}$ by adding the exponents.

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Step 5.1

Move $y^{- \frac{1}{4}}$ .

$\frac{7 (y^{- \frac{1}{4}} y^{\frac{5}{2}})}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.2

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

$\frac{7 y^{- \frac{1}{4} + \frac{5}{2}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.3

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 y^{- \frac{1}{4} + \frac{5}{2} \cdot \frac{2}{2}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.4

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

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Step 5.4.1

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

$\frac{7 y^{- \frac{1}{4} + \frac{5 \cdot 2}{2 \cdot 2}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.4.2

Multiply $2$ by $2$ .

$\frac{7 y^{- \frac{1}{4} + \frac{5 \cdot 2}{4}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.5

Combine the numerators over the common denominator.

$\frac{7 y^{\frac{- 1 + 5 \cdot 2}{4}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.6

Simplify the numerator.

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Step 5.6.1

Multiply $5$ by $2$ .

$\frac{7 y^{\frac{- 1 + 10}{4}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 5.6.2

Add $- 1$ and $10$ .

$\frac{7 y^{\frac{9}{4}}}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 6

Factor $7$ out of $7 y^{\frac{9}{4}}$ .

$\frac{7 (y^{\frac{9}{4}})}{56 x^{\frac{1}{4}} z^{\frac{2}{3}}}$

Step 7

Cancel the common factors.

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Step 7.1

Factor $7$ out of $56 x^{\frac{1}{4}} z^{\frac{2}{3}}$ .

$\frac{7 (y^{\frac{9}{4}})}{7 (8 x^{\frac{1}{4}} z^{\frac{2}{3}})}$

Step 7.2

Cancel the common factor.

$\frac{7 y^{\frac{9}{4}}}{7 (8 x^{\frac{1}{4}} z^{\frac{2}{3}})}$

Step 7.3

Rewrite the expression.

$\frac{y^{\frac{9}{4}}}{8 x^{\frac{1}{4}} z^{\frac{2}{3}}}$