Algebra Examples

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

Step 1

Cancel the common factor of $a^{2}$ and $a^{- 3}$ .

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Step 1.1

Factor $a^{- 3}$ out of $a^{2} a^{4}$ .

$\frac{a^{- 3} (a^{5} a^{4}) \div a^{- 3}}{a \div {(a^{2} a^{3})}^{4}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

$\frac{a^{- 3} (a^{5} a^{4}) \div a^{- 3} \cdot 1}{a \div {(a^{2} a^{3})}^{4}}$

Step 1.2.2

Cancel the common factor.

$\frac{a^{- 3} (a^{5} a^{4}) \div a^{- 3} \cdot 1}{a \div {(a^{2} a^{3})}^{4}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{a^{5} a^{4}}{1}}{a \div {(a^{2} a^{3})}^{4}}$

Step 1.2.4

Divide $a^{5} a^{4}$ by $1$ .

$\frac{a^{5} a^{4}}{a \div {(a^{2} a^{3})}^{4}}$

Step 2

Multiply $a^{5}$ by $a^{4}$ by adding the exponents.

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Step 2.1

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

$\frac{a^{5 + 4}}{a \div {(a^{2} a^{3})}^{4}}$

Step 2.2

Add $5$ and $4$ .

$\frac{a^{9}}{a \div {(a^{2} a^{3})}^{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$a^{9} \frac{{(a^{2} a^{3})}^{4}}{a}$

Step 4

Cancel the common factor of $a$ .

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Step 4.1

Factor $a$ out of $a^{9}$ .

$a \cdot a^{8} \frac{{(a^{2} a^{3})}^{4}}{a}$

Step 4.2

Cancel the common factor.

$a \cdot a^{8} \frac{{(a^{2} a^{3})}^{4}}{a}$

Step 4.3

Rewrite the expression.

$a^{8} {(a^{2} a^{3})}^{4}$

Step 5

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

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Step 5.1

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

$a^{8} {(a^{2 + 3})}^{4}$

Step 5.2

Add $2$ and $3$ .

$a^{8} {(a^{5})}^{4}$

Step 6

Multiply the exponents in ${(a^{5})}^{4}$ .

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Step 6.1

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

$a^{8} a^{5 \cdot 4}$

Step 6.2

Multiply $5$ by $4$ .

$a^{8} a^{20}$

Step 7

Multiply $a^{8}$ by $a^{20}$ by adding the exponents.

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Step 7.1

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

$a^{8 + 20}$

Step 7.2

Add $8$ and $20$ .

$a^{28}$