Basic Math Examples

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

Step 1

Combine $r^{3}$ and $\frac{3}{2}$ .

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

Step 2

Move $3$ to the left of $r^{3}$ .

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

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $- \frac{3 r^{3}}{2}$ .

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

Step 3.2

Apply the product rule to $\frac{3 r^{3}}{2}$ .

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

Step 3.3

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

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

Step 4

Raise $- 1$ to the power of $3$ .

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

Step 5

Simplify the numerator.

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Step 5.1

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

$- \frac{27 {(r^{3})}^{3}}{2^{3}} {(3 r)}^{2}$

Step 5.2

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

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Step 5.2.1

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

$- \frac{27 r^{3 \cdot 3}}{2^{3}} {(3 r)}^{2}$

Step 5.2.2

Multiply $3$ by $3$ .

$- \frac{27 r^{9}}{2^{3}} {(3 r)}^{2}$

Step 6

Simplify the expression.

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Step 6.1

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

$- \frac{27 r^{9}}{8} {(3 r)}^{2}$

Step 6.2

Apply the product rule to $3 r$ .

$- \frac{27 r^{9}}{8} (3^{2} r^{2})$

Step 6.3

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

$- \frac{27 r^{9}}{8} (9 r^{2})$

Step 7

Multiply $- \frac{27 r^{9}}{8} (9 r^{2})$ .

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Step 7.1

Multiply $9$ by $- 1$ .

$- 9 \frac{27 r^{9}}{8} r^{2}$

Step 7.2

Combine $- 9$ and $\frac{27 r^{9}}{8}$ .

$\frac{- 9 (27 r^{9})}{8} r^{2}$

Step 7.3

Multiply $27$ by $- 9$ .

$\frac{- 243 r^{9}}{8} r^{2}$

Step 7.4

Combine $\frac{- 243 r^{9}}{8}$ and $r^{2}$ .

$\frac{- 243 r^{9} r^{2}}{8}$

Step 7.5

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

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Step 7.5.1

Move $r^{2}$ .

$\frac{- 243 (r^{2} r^{9})}{8}$

Step 7.5.2

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

$\frac{- 243 r^{2 + 9}}{8}$

Step 7.5.3

Add $2$ and $9$ .

$\frac{- 243 r^{11}}{8}$

Step 8

Move the negative in front of the fraction.

$- \frac{243 r^{11}}{8}$