Algebra Examples

$\frac{4 r^{3} {(r^{4})}^{3}}{15 {(r^{3})}^{- 2}}$

Step 1

Move ${(r^{3})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 r^{3} {(r^{4})}^{3} {(r^{3})}^{2}}{15}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(r^{4})}^{3}$ .

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Step 2.1.1

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

$\frac{4 r^{3} r^{4 \cdot 3} {(r^{3})}^{2}}{15}$

Step 2.1.2

Multiply $4$ by $3$ .

$\frac{4 r^{3} r^{12} {(r^{3})}^{2}}{15}$

Step 2.2

Multiply the exponents in ${(r^{3})}^{2}$ .

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Step 2.2.1

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

$\frac{4 r^{3} r^{12} r^{3 \cdot 2}}{15}$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{4 r^{3} r^{12} r^{6}}{15}$

Step 2.3

Combine exponents.

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Step 2.3.1

Multiply $r^{3}$ by $r^{12}$ by adding the exponents.

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Step 2.3.1.1

Move $r^{12}$ .

$\frac{4 (r^{12} r^{3}) r^{6}}{15}$

Step 2.3.1.2

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

$\frac{4 r^{12 + 3} r^{6}}{15}$

Step 2.3.1.3

Add $12$ and $3$ .

$\frac{4 r^{15} r^{6}}{15}$

Step 2.3.2

Multiply $r^{15}$ by $r^{6}$ by adding the exponents.

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Step 2.3.2.1

Move $r^{6}$ .

$\frac{4 (r^{6} r^{15})}{15}$

Step 2.3.2.2

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

$\frac{4 r^{6 + 15}}{15}$

Step 2.3.2.3

Add $6$ and $15$ .

$\frac{4 r^{21}}{15}$