Basic Math Examples

$\frac{{(3 r)}^{2} r^{3}}{r^{- 1} r^{- 5}}$

Step 1

Multiply $r^{- 1}$ by $r^{- 5}$ by adding the exponents.

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Step 1.1

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

$\frac{{(3 r)}^{2} r^{3}}{r^{- 1 - 5}}$

Step 1.2

Subtract $5$ from $- 1$ .

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

Step 2

Move $r^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3 r)}^{2} r^{3} r^{6}$

Step 3

Multiply $r^{3}$ by $r^{6}$ by adding the exponents.

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Step 3.1

Move $r^{6}$ .

${(3 r)}^{2} (r^{6} r^{3})$

Step 3.2

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

${(3 r)}^{2} r^{6 + 3}$

Step 3.3

Add $6$ and $3$ .

${(3 r)}^{2} r^{9}$

Step 4

Apply the product rule to $3 r$ .

$3^{2} r^{2} r^{9}$

Step 5

Multiply $r^{2}$ by $r^{9}$ by adding the exponents.

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Step 5.1

Move $r^{9}$ .

$3^{2} (r^{9} r^{2})$

Step 5.2

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

$3^{2} r^{9 + 2}$

Step 5.3

Add $9$ and $2$ .

$3^{2} r^{11}$

Step 6

Raise $3$ to the power of $2$ .

$9 r^{11}$