Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.1.3

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

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

Step 4.1.4

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

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Step 4.1.4.1

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

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

Step 4.1.4.2

Multiply $2$ by $2$ .

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

Step 4.1.5

Combine the numerators over the common denominator.

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

Step 4.1.6

Add $2$ and $3$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

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

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

Step 4.2.4

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

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Step 4.2.4.1

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

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

Step 4.2.4.2

Multiply $2$ by $2$ .

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

Step 4.2.5

Combine the numerators over the common denominator.

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

Step 4.2.6

Simplify the numerator.

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Step 4.2.6.1

Multiply $5$ by $2$ .

$\frac{7 x^{\frac{5}{4}} y^{\frac{- 1 + 10}{4}} z^{\frac{2}{3}}}{56}$

Step 4.2.6.2

Add $- 1$ and $10$ .

$\frac{7 x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}}}{56}$

Step 5

Factor $7$ out of $7 x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}}$ .

$\frac{7 (x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}})}{56}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $7$ out of $56$ .

$\frac{7 (x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}})}{7 \cdot 8}$

Step 6.2

Cancel the common factor.

$\frac{7 (x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}})}{7 \cdot 8}$

Step 6.3

Rewrite the expression.

$\frac{x^{\frac{5}{4}} y^{\frac{9}{4}} z^{\frac{2}{3}}}{8}$