Basic Math Examples

$\frac{g^{- 1} a^{4} b^{4}}{g^{- 2} a^{9} y^{4}} \cdot \frac{y^{5}}{a^{2} b^{- \frac{1}{2}}}$

Step 1

Combine.

$\frac{g^{- 1} a^{4} b^{4} y^{5}}{g^{- 2} a^{9} y^{4} (a^{2} b^{- \frac{1}{2}})}$

Step 2

Multiply $a^{9}$ by $a^{2}$ by adding the exponents.

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Step 2.1

Move $a^{2}$ .

$\frac{g^{- 1} a^{4} b^{4} y^{5}}{g^{- 2} (a^{2} a^{9}) y^{4} b^{- \frac{1}{2}}}$

Step 2.2

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

$\frac{g^{- 1} a^{4} b^{4} y^{5}}{g^{- 2} a^{2 + 9} y^{4} b^{- \frac{1}{2}}}$

Step 2.3

Add $2$ and $9$ .

$\frac{g^{- 1} a^{4} b^{4} y^{5}}{g^{- 2} a^{11} y^{4} b^{- \frac{1}{2}}}$

Step 3

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

$\frac{g^{- 1} a^{4} b^{4} y^{5} g^{2}}{a^{11} y^{4} b^{- \frac{1}{2}}}$

Step 4

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

$\frac{g^{- 1} a^{4} b^{4} y^{5} g^{2} b^{\frac{1}{2}}}{a^{11} y^{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $g^{- 1}$ by $g^{2}$ by adding the exponents.

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Step 5.1.1

Move $g^{2}$ .

$\frac{g^{2} g^{- 1} a^{4} b^{4} y^{5} b^{\frac{1}{2}}}{a^{11} y^{4}}$

Step 5.1.2

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

$\frac{g^{2 - 1} a^{4} b^{4} y^{5} b^{\frac{1}{2}}}{a^{11} y^{4}}$

Step 5.1.3

Subtract $1$ from $2$ .

$\frac{g^{1} a^{4} b^{4} y^{5} b^{\frac{1}{2}}}{a^{11} y^{4}}$

Step 5.2

Simplify $g^{1} a^{4} b^{4} y^{5}$ .

$\frac{g a^{4} b^{4} y^{5} b^{\frac{1}{2}}}{a^{11} y^{4}}$

Step 5.3

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

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Step 5.3.1

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

$\frac{g a^{4} (b^{\frac{1}{2}} b^{4}) y^{5}}{a^{11} y^{4}}$

Step 5.3.2

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

$\frac{g a^{4} b^{\frac{1}{2} + 4} y^{5}}{a^{11} y^{4}}$

Step 5.3.3

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{g a^{4} b^{\frac{1}{2} + 4 \cdot \frac{2}{2}} y^{5}}{a^{11} y^{4}}$

Step 5.3.4

Combine $4$ and $\frac{2}{2}$ .

$\frac{g a^{4} b^{\frac{1}{2} + \frac{4 \cdot 2}{2}} y^{5}}{a^{11} y^{4}}$

Step 5.3.5

Combine the numerators over the common denominator.

$\frac{g a^{4} b^{\frac{1 + 4 \cdot 2}{2}} y^{5}}{a^{11} y^{4}}$

Step 5.3.6

Simplify the numerator.

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Step 5.3.6.1

Multiply $4$ by $2$ .

$\frac{g a^{4} b^{\frac{1 + 8}{2}} y^{5}}{a^{11} y^{4}}$

Step 5.3.6.2

Add $1$ and $8$ .

$\frac{g a^{4} b^{\frac{9}{2}} y^{5}}{a^{11} y^{4}}$

Step 6

Factor $a^{4}$ out of $g a^{4} b^{\frac{9}{2}} y^{5}$ .

$\frac{a^{4} (g b^{\frac{9}{2}} y^{5})}{a^{11} y^{4}}$

Step 7

Cancel the common factors.

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Step 7.1

Factor $a^{4}$ out of $a^{11} y^{4}$ .

$\frac{a^{4} (g b^{\frac{9}{2}} y^{5})}{a^{4} (a^{7} y^{4})}$

Step 7.2

Cancel the common factor.

$\frac{a^{4} (g b^{\frac{9}{2}} y^{5})}{a^{4} (a^{7} y^{4})}$

Step 7.3

Rewrite the expression.

$\frac{g b^{\frac{9}{2}} y^{5}}{a^{7} y^{4}}$

Step 8

Factor $y^{4}$ out of $g b^{\frac{9}{2}} y^{5}$ .

$\frac{y^{4} (g b^{\frac{9}{2}} y)}{a^{7} y^{4}}$

Step 9

Cancel the common factors.

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Step 9.1

Factor $y^{4}$ out of $a^{7} y^{4}$ .

$\frac{y^{4} (g b^{\frac{9}{2}} y)}{y^{4} a^{7}}$

Step 9.2

Cancel the common factor.

$\frac{y^{4} (g b^{\frac{9}{2}} y)}{y^{4} a^{7}}$

Step 9.3

Rewrite the expression.

$\frac{g b^{\frac{9}{2}} y}{a^{7}}$

Step 10

Reorder factors in $\frac{g b^{\frac{9}{2}} y}{a^{7}}$ .

$\frac{g y b^{\frac{9}{2}}}{a^{7}}$