Basic Math Examples

$3 y^{2} + \frac{9 y}{18} \div 5 y^{\frac{2}{27}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$3 y^{2} + \frac{\frac{9 y}{18}}{5 y^{\frac{2}{27}}}$

Step 1.2

Cancel the common factor of $9$ and $18$ .

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Step 1.2.1

Factor $9$ out of $9 y$ .

$3 y^{2} + \frac{\frac{9 (y)}{18}}{5 y^{\frac{2}{27}}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $9$ out of $18$ .

$3 y^{2} + \frac{\frac{9 y}{9 \cdot 2}}{5 y^{\frac{2}{27}}}$

Step 1.2.2.2

Cancel the common factor.

$3 y^{2} + \frac{\frac{9 y}{9 \cdot 2}}{5 y^{\frac{2}{27}}}$

Step 1.2.2.3

Rewrite the expression.

$3 y^{2} + \frac{\frac{y}{2}}{5 y^{\frac{2}{27}}}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$3 y^{2} + \frac{y}{2} \cdot \frac{1}{5 y^{\frac{2}{27}}}$

Step 1.4

Combine.

$3 y^{2} + \frac{y \cdot 1}{2 (5 y^{\frac{2}{27}})}$

Step 1.5

Move $y^{\frac{2}{27}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3 y^{2} + \frac{y \cdot y^{- \frac{2}{27}}}{2 \cdot 5}$

Step 1.6

Multiply $y$ by $y^{- \frac{2}{27}}$ by adding the exponents.

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Step 1.6.1

Multiply $y$ by $y^{- \frac{2}{27}}$ .

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Step 1.6.1.1

Raise $y$ to the power of $1$ .

$3 y^{2} + \frac{y^{1} y^{- \frac{2}{27}}}{2 \cdot 5}$

Step 1.6.1.2

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

$3 y^{2} + \frac{y^{1 - \frac{2}{27}}}{2 \cdot 5}$

Step 1.6.2

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

$3 y^{2} + \frac{y^{\frac{27}{27} - \frac{2}{27}}}{2 \cdot 5}$

Step 1.6.3

Combine the numerators over the common denominator.

$3 y^{2} + \frac{y^{\frac{27 - 2}{27}}}{2 \cdot 5}$

Step 1.6.4

Subtract $2$ from $27$ .

$3 y^{2} + \frac{y^{\frac{25}{27}}}{2 \cdot 5}$

Step 1.7

Multiply $2$ by $5$ .

$3 y^{2} + \frac{y^{\frac{25}{27}}}{10}$

Step 2

To write $3 y^{2}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$3 y^{2} \cdot \frac{10}{10} + \frac{y^{\frac{25}{27}}}{10}$

Step 3

Simplify terms.

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Step 3.1

Combine $3 y^{2}$ and $\frac{10}{10}$ .

$\frac{3 y^{2} \cdot 10}{10} + \frac{y^{\frac{25}{27}}}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 y^{2} \cdot 10 + y^{\frac{25}{27}}}{10}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $y^{\frac{25}{27}}$ out of $3 y^{2} \cdot 10 + y^{\frac{25}{27}}$ .

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Step 4.1.1

Move $y^{2}$ .

$\frac{3 \cdot 10 y^{2} + y^{\frac{25}{27}}}{10}$

Step 4.1.2

Factor $y^{\frac{25}{27}}$ out of $3 \cdot 10 y^{2}$ .

$\frac{y^{\frac{25}{27}} (3 \cdot 10 y^{\frac{29}{27}}) + y^{\frac{25}{27}}}{10}$

Step 4.1.3

Multiply by $1$ .

$\frac{y^{\frac{25}{27}} (3 \cdot 10 y^{\frac{29}{27}}) + y^{\frac{25}{27}} \cdot 1}{10}$

Step 4.1.4

Factor $y^{\frac{25}{27}}$ out of $y^{\frac{25}{27}} (3 \cdot 10 y^{\frac{29}{27}}) + y^{\frac{25}{27}} \cdot 1$ .

$\frac{y^{\frac{25}{27}} (3 \cdot 10 y^{\frac{29}{27}} + 1)}{10}$

Step 4.2

Multiply $3$ by $10$ .

$\frac{y^{\frac{25}{27}} (30 y^{\frac{29}{27}} + 1)}{10}$