Basic Math Examples

$3 \cdot y^{- \frac{1}{5}} \cdot y^{\frac{7}{10}}$

Step 1

Move $y^{\frac{7}{10}}$ .

$3 \cdot (y^{\frac{7}{10}} y^{- \frac{1}{5}})$

Step 2

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

$3 \cdot y^{\frac{7}{10} - \frac{1}{5}}$

Step 3

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

$3 \cdot y^{\frac{7}{10} - \frac{1}{5} \cdot \frac{2}{2}}$

Step 4

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

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Step 4.1

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

$3 \cdot y^{\frac{7}{10} - \frac{2}{5 \cdot 2}}$

Step 4.2

Multiply $5$ by $2$ .

$3 \cdot y^{\frac{7}{10} - \frac{2}{10}}$

Step 5

Combine the numerators over the common denominator.

$3 \cdot y^{\frac{7 - 2}{10}}$

Step 6

Subtract $2$ from $7$ .

$3 \cdot y^{\frac{5}{10}}$

Step 7

Cancel the common factor of $5$ and $10$ .

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Step 7.1

Factor $5$ out of $5$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $5$ out of $10$ .

$3 \cdot y^{\frac{5 \cdot 1}{5 \cdot 2}}$

Step 7.2.2

Cancel the common factor.

$3 \cdot y^{\frac{5 \cdot 1}{5 \cdot 2}}$

Step 7.2.3

Rewrite the expression.

$3 \cdot y^{\frac{1}{2}}$

$3 y^{\frac{1}{2}}$