Algebra Examples

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

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

Step 1

Cancel the common factor of

a^{2}

$a^{2}$ and

a^{- 3}

$a^{- 3}$ .

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Step 1.1

Factor

a^{- 3}

$a^{- 3}$ out of

a^{2} a^{4}

$a^{2} a^{4}$ .

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

$1$ .

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

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

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}}

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

Step 1.2.3

Rewrite the expression.

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

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

Step 1.2.4

Divide

a^{5} a^{4}

$a^{5} a^{4}$ by

1

$1$ .

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

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

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

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

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

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

Step 2

Multiply

a^{5}

$a^{5}$ by

a^{4}

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

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Step 2.1

Use the power rule

a^{m} a^{n} = a^{m + n}

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

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

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

Step 2.2

Add

5

$5$ and

4

$4$ .

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

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

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

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

Step 4

Cancel the common factor of

a

$a$ .

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Step 4.1

Factor

a

$a$ out of

a^{9}

$a^{9}$ .

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

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

Step 4.2

Cancel the common factor.

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

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

Step 4.3

Rewrite the expression.

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

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

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

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

Step 5

Multiply

a^{2}

$a^{2}$ by

a^{3}

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

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Step 5.1

Use the power rule

a^{m} a^{n} = a^{m + n}

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

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

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

Step 5.2

Add

2

$2$ and

3

$3$ .

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

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

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

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

Step 6

Multiply the exponents in

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

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

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Step 6.1

Apply the power rule and multiply exponents,

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

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

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

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

Step 6.2

Multiply

5

$5$ by

4

$4$ .

a^{8} a^{20}

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

a^{8} a^{20}

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

Step 7

Multiply

a^{8}

$a^{8}$ by

a^{20}

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

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Step 7.1

Use the power rule

a^{m} a^{n} = a^{m + n}

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

a^{8 + 20}

$a^{8 + 20}$

Step 7.2

Add

8

$8$ and

20

$20$ .

a^{28}

$a^{28}$

a^{28}

$a^{28}$