Basic Math Examples

{(- 3 r^{4} r^{- 3} \div r^{- 3} r^{7})}^{3}

${(- 3 r^{4} r^{- 3} \div r^{- 3} r^{7})}^{3}$

Step 1

Rewrite the division as a fraction.

{(\frac{- 3 r^{4} r^{- 3}}{r^{- 3} r^{7}})}^{3}

${(\frac{- 3 r^{4} r^{- 3}}{r^{- 3} r^{7}})}^{3}$

Step 2

Multiply

$r^{4}$ by

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

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Step 2.1

Move

$r^{- 3}$ .

${(\frac{- 3 (r^{- 3} r^{4})}{r^{- 3} r^{7}})}^{3}$

Step 2.2

Use the power rule

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

${(\frac{- 3 r^{- 3 + 4}}{r^{- 3} r^{7}})}^{3}$

Step 2.3

Add

$- 3$ and

$4$ .

${(\frac{- 3 r^{1}}{r^{- 3} r^{7}})}^{3}$

${(\frac{- 3 r^{1}}{r^{- 3} r^{7}})}^{3}$

Step 3

Simplify

$- 3 r^{1}$ .

${(\frac{- 3 r}{r^{- 3} r^{7}})}^{3}$

Step 4

Multiply

$r^{- 3}$ by

$r^{7}$ by adding the exponents.

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Step 4.1

Use the power rule

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

${(\frac{- 3 r}{r^{- 3 + 7}})}^{3}$

Step 4.2

Add

$- 3$ and

$7$ .

${(\frac{- 3 r}{r^{4}})}^{3}$

${(\frac{- 3 r}{r^{4}})}^{3}$

Step 5

Cancel the common factor of

$r$ and

$r^{4}$ .

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Step 5.1

Factor

$r$ out of

$- 3 r$ .

${(\frac{r \cdot - 3}{r^{4}})}^{3}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$r$ out of

$r^{4}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

Move the negative in front of the fraction.

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

Step 7

Use the power rule

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

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Step 7.1

Apply the product rule to

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

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

Step 7.2

Apply the product rule to

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

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

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

Step 8

Raise

$- 1$ to the power of

$3$ .

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

Step 9

Raise

$3$ to the power of

$3$ .

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

Step 10

Multiply the exponents in

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

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Step 10.1

Apply the power rule and multiply exponents,

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

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

Step 10.2

Multiply

$3$ by

$3$ .

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

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

${(- 3 r^{4} r^{- 3} \div r^{- 3} r^{7})}^{3}$

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