Basic Math Examples

$y^{- \frac{11}{20}} \cdot y^{\frac{4}{5}} \cdot y^{\frac{3}{4}}$

Step 1

Multiply $y^{- \frac{11}{20}}$ by $y^{\frac{4}{5}}$ by adding the exponents.

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Step 1.1

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

$y^{- \frac{11}{20} + \frac{4}{5}} \cdot y^{\frac{3}{4}}$

Step 1.2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y^{- \frac{11}{20} + \frac{4}{5} \cdot \frac{4}{4}} \cdot y^{\frac{3}{4}}$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$y^{- \frac{11}{20} + \frac{4 \cdot 4}{5 \cdot 4}} \cdot y^{\frac{3}{4}}$

Step 1.3.2

Multiply $5$ by $4$ .

$y^{- \frac{11}{20} + \frac{4 \cdot 4}{20}} \cdot y^{\frac{3}{4}}$

Step 1.4

Combine the numerators over the common denominator.

$y^{\frac{- 11 + 4 \cdot 4}{20}} \cdot y^{\frac{3}{4}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $4$ .

$y^{\frac{- 11 + 16}{20}} \cdot y^{\frac{3}{4}}$

Step 1.5.2

Add $- 11$ and $16$ .

$y^{\frac{5}{20}} \cdot y^{\frac{3}{4}}$

Step 1.6

Cancel the common factor of $5$ and $20$ .

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Step 1.6.1

Factor $5$ out of $5$ .

$y^{\frac{5 (1)}{20}} \cdot y^{\frac{3}{4}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $5$ out of $20$ .

$y^{\frac{5 \cdot 1}{5 \cdot 4}} \cdot y^{\frac{3}{4}}$

Step 1.6.2.2

Cancel the common factor.

$y^{\frac{5 \cdot 1}{5 \cdot 4}} \cdot y^{\frac{3}{4}}$

Step 1.6.2.3

Rewrite the expression.

$y^{\frac{1}{4}} \cdot y^{\frac{3}{4}}$

Step 2

Multiply $y^{\frac{1}{4}}$ by $y^{\frac{3}{4}}$ 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.

$y^{\frac{1}{4} + \frac{3}{4}}$

Step 2.2

Combine the numerators over the common denominator.

$y^{\frac{1 + 3}{4}}$

Step 2.3

Add $1$ and $3$ .

$y^{\frac{4}{4}}$

Step 2.4

Divide $4$ by $4$ .

$y^{1}$

Step 3

Simplify $y^{1}$ .

$y$