Basic Math Examples

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

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

Step 1

Combine

r^{3}

$r^{3}$ and

\frac{3}{2}

$\frac{3}{2}$ .

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

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

Step 2

Move

3

$3$ to the left of

r^{3}

$r^{3}$ .

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

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

Step 3

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 3.1

Apply the product rule to

- \frac{3 r^{3}}{2}

$- \frac{3 r^{3}}{2}$ .

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

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

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

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

Step 3.3

Apply the product rule to

3 r^{3}

$3 r^{3}$ .

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

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

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

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

Step 4

Raise

- 1

$- 1$ to the power of

3

$3$ .

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

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

Step 5

Simplify the numerator.

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Step 5.1

Raise

3

$3$ to the power of

3

$3$ .

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

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

Step 5.2

Multiply the exponents in

{(r^{3})}^{3}

${(r^{3})}^{3}$ .

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Step 5.2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 5.2.2

Multiply

3

$3$ by

3

$3$ .

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

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

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

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

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

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

Step 6

Simplify the expression.

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Step 6.1

Raise

2

$2$ to the power of

3

$3$ .

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

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

Step 6.2

Apply the product rule to

3 r

$3 r$ .

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

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

Step 6.3

Raise

3

$3$ to the power of

2

$2$ .

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

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

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

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

Step 7

Multiply

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

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

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Step 7.1

Multiply

9

$9$ by

- 1

$- 1$ .

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

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

Step 7.2

Combine

- 9

$- 9$ and

\frac{27 r^{9}}{8}

$\frac{27 r^{9}}{8}$ .

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

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

Step 7.3

Multiply

27

$27$ by

- 9

$- 9$ .

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

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

Step 7.4

Combine

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

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

r^{2}

$r^{2}$ .

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

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

Step 7.5

Multiply

r^{9}

$r^{9}$ by

r^{2}

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

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Step 7.5.1

Move

r^{2}

$r^{2}$ .

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

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

Step 7.5.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 7.5.3

Add

2

$2$ and

9

$9$ .

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

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

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

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

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

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

Step 8

Move the negative in front of the fraction.

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

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