Basic Math Examples

$\frac{- 9}{\sqrt[3]{49 y^{2}}}$

Step 1

Move the negative in front of the fraction.

$- \frac{9}{\sqrt[3]{49 y^{2}}}$

Step 2

Multiply $\frac{9}{\sqrt[3]{49 y^{2}}}$ by $\frac{{\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{2}}$ .

$- (\frac{9}{\sqrt[3]{49 y^{2}}} \cdot \frac{{\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{2}})$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{9}{\sqrt[3]{49 y^{2}}}$ by $\frac{{\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{2}}$ .

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{\sqrt[3]{49 y^{2}} {\sqrt[3]{49 y^{2}}}^{2}}$

Step 3.2

Raise $\sqrt[3]{49 y^{2}}$ to the power of $1$ .

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{1} {\sqrt[3]{49 y^{2}}}^{2}}$

Step 3.3

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

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{1 + 2}}$

Step 3.4

Add $1$ and $2$ .

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{\sqrt[3]{49 y^{2}}}^{3}}$

Step 3.5

Rewrite ${\sqrt[3]{49 y^{2}}}^{3}$ as $49 y^{2}$ .

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Step 3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{49 y^{2}}$ as ${(49 y^{2})}^{\frac{1}{3}}$ .

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{({(49 y^{2})}^{\frac{1}{3}})}^{3}}$

Step 3.5.2

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

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{(49 y^{2})}^{\frac{1}{3} \cdot 3}}$

Step 3.5.3

Combine $\frac{1}{3}$ and $3$ .

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{(49 y^{2})}^{\frac{3}{3}}}$

Step 3.5.4

Cancel the common factor of $3$ .

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Step 3.5.4.1

Cancel the common factor.

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{(49 y^{2})}^{\frac{3}{3}}}$

Step 3.5.4.2

Rewrite the expression.

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{{(49 y^{2})}^{1}}$

Step 3.5.5

Simplify.

$- \frac{9 {\sqrt[3]{49 y^{2}}}^{2}}{49 y^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite ${\sqrt[3]{49 y^{2}}}^{2}$ as $\sqrt[3]{{(49 y^{2})}^{2}}$ .

$- \frac{9 \sqrt[3]{{(49 y^{2})}^{2}}}{49 y^{2}}$

Step 4.2

Apply the product rule to $49 y^{2}$ .

$- \frac{9 \sqrt[3]{49^{2} {(y^{2})}^{2}}}{49 y^{2}}$

Step 4.3

Raise $49$ to the power of $2$ .

$- \frac{9 \sqrt[3]{2401 {(y^{2})}^{2}}}{49 y^{2}}$

Step 4.4

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

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Step 4.4.1

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

$- \frac{9 \sqrt[3]{2401 y^{2 \cdot 2}}}{49 y^{2}}$

Step 4.4.2

Multiply $2$ by $2$ .

$- \frac{9 \sqrt[3]{2401 y^{4}}}{49 y^{2}}$

Step 4.5

Rewrite $2401 y^{4}$ as ${(7 y)}^{3} \cdot (7 y)$ .

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Step 4.5.1

Factor $343$ out of $2401$ .

$- \frac{9 \sqrt[3]{343 (7) y^{4}}}{49 y^{2}}$

Step 4.5.2

Rewrite $343$ as $7^{3}$ .

$- \frac{9 \sqrt[3]{7^{3} \cdot 7 y^{4}}}{49 y^{2}}$

Step 4.5.3

Factor out $y^{3}$ .

$- \frac{9 \sqrt[3]{7^{3} \cdot 7 (y^{3} y)}}{49 y^{2}}$

Step 4.5.4

Move $7$ .

$- \frac{9 \sqrt[3]{7^{3} y^{3} \cdot 7 y}}{49 y^{2}}$

Step 4.5.5

Rewrite $7^{3} y^{3}$ as ${(7 y)}^{3}$ .

$- \frac{9 \sqrt[3]{{(7 y)}^{3} \cdot 7 y}}{49 y^{2}}$

Step 4.5.6

Add parentheses.

$- \frac{9 \sqrt[3]{{(7 y)}^{3} \cdot (7 y)}}{49 y^{2}}$

Step 4.6

Pull terms out from under the radical.

$- \frac{9 \cdot 7 y \sqrt[3]{7 y}}{49 y^{2}}$

Step 4.7

Multiply $9$ by $7$ .

$- \frac{63 y \sqrt[3]{7 y}}{49 y^{2}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $63$ and $49$ .

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Step 5.1.1

Factor $7$ out of $63 y \sqrt[3]{7 y}$ .

$- \frac{7 (9 y \sqrt[3]{7 y})}{49 y^{2}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $7$ out of $49 y^{2}$ .

$- \frac{7 (9 y \sqrt[3]{7 y})}{7 (7 y^{2})}$

Step 5.1.2.2

Cancel the common factor.

$- \frac{7 (9 y \sqrt[3]{7 y})}{7 (7 y^{2})}$

Step 5.1.2.3

Rewrite the expression.

$- \frac{9 y \sqrt[3]{7 y}}{7 y^{2}}$

Step 5.2

Cancel the common factor of $y$ and $y^{2}$ .

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Step 5.2.1

Factor $y$ out of $9 y \sqrt[3]{7 y}$ .

$- \frac{y (9 \sqrt[3]{7 y})}{7 y^{2}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $y$ out of $7 y^{2}$ .

$- \frac{y (9 \sqrt[3]{7 y})}{y (7 y)}$

Step 5.2.2.2

Cancel the common factor.

$- \frac{y (9 \sqrt[3]{7 y})}{y (7 y)}$

Step 5.2.2.3

Rewrite the expression.

$- \frac{9 \sqrt[3]{7 y}}{7 y}$