Basic Math Examples

$\frac{y^{\frac{1}{2}}}{{(y^{2})}^{- \frac{1}{2}}} \cdot \frac{y^{\frac{2}{5}}}{y^{- \frac{3}{10}}}$

Step 1

Combine.

$\frac{y^{\frac{1}{2}} y^{\frac{2}{5}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2

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

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Step 2.1

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

$\frac{y^{\frac{1}{2} + \frac{2}{5}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y^{\frac{1}{2} \cdot \frac{5}{5} + \frac{2}{5}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.3

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

$\frac{y^{\frac{1}{2} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{2}{2}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{y^{\frac{5}{2 \cdot 5} + \frac{2}{5} \cdot \frac{2}{2}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.4.2

Multiply $2$ by $5$ .

$\frac{y^{\frac{5}{10} + \frac{2}{5} \cdot \frac{2}{2}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.4.3

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

$\frac{y^{\frac{5}{10} + \frac{2 \cdot 2}{5 \cdot 2}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.4.4

Multiply $5$ by $2$ .

$\frac{y^{\frac{5}{10} + \frac{2 \cdot 2}{10}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{y^{\frac{5 + 2 \cdot 2}{10}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $2$ by $2$ .

$\frac{y^{\frac{5 + 4}{10}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 2.6.2

Add $5$ and $4$ .

$\frac{y^{\frac{9}{10}}}{{(y^{2})}^{- \frac{1}{2}} y^{- \frac{3}{10}}}$

Step 3

Move $y^{- \frac{3}{10}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{\frac{9}{10}} y^{\frac{3}{10}}}{{(y^{2})}^{- \frac{1}{2}}}$

Step 4

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

$y^{\frac{9}{10}} y^{\frac{3}{10}} {(y^{2})}^{\frac{1}{2}}$

Step 5

Multiply $y^{\frac{9}{10}}$ by $y^{\frac{3}{10}}$ by adding the exponents.

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Step 5.1

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

$y^{\frac{9}{10} + \frac{3}{10}} {(y^{2})}^{\frac{1}{2}}$

Step 5.2

Combine the numerators over the common denominator.

$y^{\frac{9 + 3}{10}} {(y^{2})}^{\frac{1}{2}}$

Step 5.3

Add $9$ and $3$ .

$y^{\frac{12}{10}} {(y^{2})}^{\frac{1}{2}}$

Step 5.4

Cancel the common factor of $12$ and $10$ .

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Step 5.4.1

Factor $2$ out of $12$ .

$y^{\frac{2 (6)}{10}} {(y^{2})}^{\frac{1}{2}}$

Step 5.4.2

Cancel the common factors.

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Step 5.4.2.1

Factor $2$ out of $10$ .

$y^{\frac{2 \cdot 6}{2 \cdot 5}} {(y^{2})}^{\frac{1}{2}}$

Step 5.4.2.2

Cancel the common factor.

$y^{\frac{2 \cdot 6}{2 \cdot 5}} {(y^{2})}^{\frac{1}{2}}$

Step 5.4.2.3

Rewrite the expression.

$y^{\frac{6}{5}} {(y^{2})}^{\frac{1}{2}}$

Step 6

Multiply the exponents in ${(y^{2})}^{\frac{1}{2}}$ .

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Step 6.1

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

$y^{\frac{6}{5}} y^{2 (\frac{1}{2})}$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Cancel the common factor.

$y^{\frac{6}{5}} y^{2 (\frac{1}{2})}$

Step 6.2.2

Rewrite the expression.

$y^{\frac{6}{5}} y^{1}$

Step 7

Multiply $y^{\frac{6}{5}}$ by $y^{1}$ by adding the exponents.

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Step 7.1

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

$y^{\frac{6}{5} + 1}$

Step 7.2

Write $1$ as a fraction with a common denominator.

$y^{\frac{6}{5} + \frac{5}{5}}$

Step 7.3

Combine the numerators over the common denominator.

$y^{\frac{6 + 5}{5}}$

Step 7.4

Add $6$ and $5$ .

$y^{\frac{11}{5}}$