Algebra Examples

${(\frac{2 a^{5} b^{3}}{a^{3} a^{- 2}})}^{3}$

Step 1

Multiply $a^{3}$ by $a^{- 2}$ by adding the exponents.

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Step 1.1

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

${(\frac{2 a^{5} b^{3}}{a^{3 - 2}})}^{3}$

Step 1.2

Subtract $2$ from $3$ .

${(\frac{2 a^{5} b^{3}}{a^{1}})}^{3}$

Step 2

Simplify $a^{1}$ .

${(\frac{2 a^{5} b^{3}}{a})}^{3}$

Step 3

Cancel the common factor of $a^{5}$ and $a$ .

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Step 3.1

Factor $a$ out of $2 a^{5} b^{3}$ .

${(\frac{a (2 a^{4} b^{3})}{a})}^{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $a$ to the power of $1$ .

${(\frac{a (2 a^{4} b^{3})}{a^{1}})}^{3}$

Step 3.2.2

Factor $a$ out of $a^{1}$ .

${(\frac{a (2 a^{4} b^{3})}{a \cdot 1})}^{3}$

Step 3.2.3

Cancel the common factor.

${(\frac{a (2 a^{4} b^{3})}{a \cdot 1})}^{3}$

Step 3.2.4

Rewrite the expression.

${(\frac{2 a^{4} b^{3}}{1})}^{3}$

Step 3.2.5

Divide $2 a^{4} b^{3}$ by $1$ .

${(2 a^{4} b^{3})}^{3}$

Step 4

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

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Step 4.1

Apply the product rule to $2 a^{4} b^{3}$ .

${(2 a^{4})}^{3} {(b^{3})}^{3}$

Step 4.2

Apply the product rule to $2 a^{4}$ .

$2^{3} {(a^{4})}^{3} {(b^{3})}^{3}$

Step 5

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

$8 {(a^{4})}^{3} {(b^{3})}^{3}$

Step 6

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

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Step 6.1

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

$8 a^{4 \cdot 3} {(b^{3})}^{3}$

Step 6.2

Multiply $4$ by $3$ .

$8 a^{12} {(b^{3})}^{3}$

Step 7

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

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Step 7.1

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

$8 a^{12} b^{3 \cdot 3}$

Step 7.2

Multiply $3$ by $3$ .

$8 a^{12} b^{9}$