Pre-Algebra Examples

$\frac{y^{\frac{1}{10}}}{y^{\frac{1}{20}}}$

Step 1

Move $y^{\frac{1}{20}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{\frac{1}{10}} y^{- \frac{1}{20}}$

Step 2

Multiply $y^{\frac{1}{10}}$ by $y^{- \frac{1}{20}}$ 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.

$y^{\frac{1}{10} - \frac{1}{20}}$

Step 2.2

To write $\frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y^{\frac{1}{10} \cdot \frac{2}{2} - \frac{1}{20}}$

Step 2.3

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

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Step 2.3.1

Multiply $\frac{1}{10}$ by $\frac{2}{2}$ .

$y^{\frac{2}{10 \cdot 2} - \frac{1}{20}}$

Step 2.3.2

Multiply $10$ by $2$ .

$y^{\frac{2}{20} - \frac{1}{20}}$

Step 2.4

Combine the numerators over the common denominator.

$y^{\frac{2 - 1}{20}}$

Step 2.5

Subtract $1$ from $2$ .

$y^{\frac{1}{20}}$