Basic Math Examples

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

Step 1

Rewrite the division as a fraction.

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

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 $4$ .

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

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 $7$ .

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

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.

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

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

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

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 $3$ .

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