Basic Math Examples

${(\frac{9 r^{3} y^{- 2} \cdot (2 r^{- 4} y^{3})}{6 r^{2} y})}^{3}$

Step 1

Multiply $r^{3}$ by $r^{- 4}$ by adding the exponents.

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Step 1.1

Move $r^{- 4}$ .

${(\frac{9 (r^{- 4} r^{3}) y^{- 2} \cdot (2 y^{3})}{6 r^{2} y})}^{3}$

Step 1.2

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

${(\frac{9 r^{- 4 + 3} y^{- 2} \cdot (2 y^{3})}{6 r^{2} y})}^{3}$

Step 1.3

Add $- 4$ and $3$ .

${(\frac{9 r^{- 1} y^{- 2} \cdot (2 y^{3})}{6 r^{2} y})}^{3}$

Step 2

Multiply $y^{- 2}$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

${(\frac{9 r^{- 1} (y^{3} y^{- 2}) \cdot 2}{6 r^{2} y})}^{3}$

Step 2.2

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

${(\frac{9 r^{- 1} y^{3 - 2} \cdot 2}{6 r^{2} y})}^{3}$

Step 2.3

Subtract $2$ from $3$ .

${(\frac{9 r^{- 1} y^{1} \cdot 2}{6 r^{2} y})}^{3}$

Step 3

Simplify $9 r^{- 1} y^{1} \cdot 2$ .

${(\frac{9 r^{- 1} y \cdot 2}{6 r^{2} y})}^{3}$

Step 4

Move $r^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{9 y \cdot 2}{6 r^{2} y r})}^{3}$

Step 5

Multiply $r^{2}$ by $r$ by adding the exponents.

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Step 5.1

Move $r$ .

${(\frac{9 y \cdot 2}{6 (r \cdot r^{2}) y})}^{3}$

Step 5.2

Multiply $r$ by $r^{2}$ .

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Step 5.2.1

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

${(\frac{9 y \cdot 2}{6 (r^{1} r^{2}) y})}^{3}$

Step 5.2.2

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

${(\frac{9 y \cdot 2}{6 r^{1 + 2} y})}^{3}$

Step 5.3

Add $1$ and $2$ .

${(\frac{9 y \cdot 2}{6 r^{3} y})}^{3}$

Step 6

Cancel the common factor of $9$ and $6$ .

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Step 6.1

Factor $3$ out of $9 y \cdot 2$ .

${(\frac{3 (3 y \cdot 2)}{6 r^{3} y})}^{3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $6 r^{3} y$ .

${(\frac{3 (3 y \cdot 2)}{3 (2 r^{3} y)})}^{3}$

Step 6.2.2

Cancel the common factor.

${(\frac{3 (3 y \cdot 2)}{3 (2 r^{3} y)})}^{3}$

Step 6.2.3

Rewrite the expression.

${(\frac{3 y \cdot 2}{2 r^{3} y})}^{3}$

Step 7

Cancel the common factor of $y$ .

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Step 7.1

Cancel the common factor.

${(\frac{3 y \cdot 2}{2 r^{3} y})}^{3}$

Step 7.2

Rewrite the expression.

${(\frac{3 \cdot 2}{2 r^{3}})}^{3}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Cancel the common factor.

${(\frac{3 \cdot 2}{2 r^{3}})}^{3}$

Step 8.2

Rewrite the expression.

${(\frac{3}{r^{3}})}^{3}$

Step 9

Simplify the expression.

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Step 9.1

Apply the product rule to $\frac{3}{r^{3}}$ .

$\frac{3^{3}}{{(r^{3})}^{3}}$

Step 9.2

Raise $3$ to the power of $3$ .

$\frac{27}{{(r^{3})}^{3}}$

Step 9.3

Multiply the exponents in ${(r^{3})}^{3}$ .

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Step 9.3.1

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

$\frac{27}{r^{3 \cdot 3}}$

Step 9.3.2

Multiply $3$ by $3$ .

$\frac{27}{r^{9}}$