Pre-Algebra Examples

$\frac{(2^{3}) (3^{7}) (2^{- 4}) (3^{6})}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8})} \div \frac{2^{6} (3^{- 3})}{3^{- 2} (2^{5})}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{(2^{3}) (3^{7}) (2^{- 4}) (3^{6})}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8})} \cdot \frac{3^{- 2} (2^{5})}{2^{6} (3^{- 3})}$

Step 2

Combine.

$\frac{(2^{3}) (3^{7}) (2^{- 4}) (3^{6}) (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 3

Multiply $2^{3}$ by $2^{- 4}$ by adding the exponents.

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Step 3.1

Move $2^{- 4}$ .

$\frac{2^{- 4} \cdot 2^{3} \cdot 3^{7} \cdot 3^{6} (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 3.2

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

$\frac{2^{- 4 + 3} \cdot 3^{7} \cdot 3^{6} (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 3.3

Add $- 4$ and $3$ .

$\frac{2^{- 1} \cdot 3^{7} \cdot 3^{6} (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 4

Multiply $3^{7}$ by $3^{6}$ by adding the exponents.

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Step 4.1

Move $3^{6}$ .

$\frac{2^{- 1} \cdot (3^{6} \cdot 3^{7}) (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 4.2

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

$\frac{2^{- 1} \cdot 3^{6 + 7} (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 4.3

Add $6$ and $7$ .

$\frac{2^{- 1} \cdot 3^{13} (3^{- 2} (2^{5}))}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 5

Multiply $2^{- 1}$ by $2^{5}$ by adding the exponents.

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Step 5.1

Move $2^{5}$ .

$\frac{2^{5} \cdot 2^{- 1} \cdot 3^{13} \cdot 3^{- 2}}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 5.2

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

$\frac{2^{5 - 1} \cdot 3^{13} \cdot 3^{- 2}}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 5.3

Subtract $1$ from $5$ .

$\frac{2^{4} \cdot 3^{13} \cdot 3^{- 2}}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 6

Multiply $3^{13}$ by $3^{- 2}$ by adding the exponents.

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Step 6.1

Move $3^{- 2}$ .

$\frac{2^{4} \cdot (3^{- 2} \cdot 3^{13})}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 6.2

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

$\frac{2^{4} \cdot 3^{- 2 + 13}}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 6.3

Add $- 2$ and $13$ .

$\frac{2^{4} \cdot 3^{11}}{(2^{2}) (2^{10}) (3^{- 3}) (2^{8}) (2^{6} (3^{- 3}))}$

Step 7

Multiply $2^{2}$ by $2^{10}$ 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.

$\frac{2^{4} \cdot 3^{11}}{2^{2 + 10} \cdot 3^{- 3} \cdot 2^{8} (2^{6} (3^{- 3}))}$

Step 7.2

Add $2$ and $10$ .

$\frac{2^{4} \cdot 3^{11}}{2^{12} \cdot 3^{- 3} \cdot 2^{8} (2^{6} (3^{- 3}))}$

Step 8

Multiply $2^{12}$ by $2^{8}$ by adding the exponents.

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Step 8.1

Move $2^{8}$ .

$\frac{2^{4} \cdot 3^{11}}{2^{8} \cdot 2^{12} \cdot 3^{- 3} (2^{6} (3^{- 3}))}$

Step 8.2

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

$\frac{2^{4} \cdot 3^{11}}{2^{8 + 12} \cdot 3^{- 3} (2^{6} (3^{- 3}))}$

Step 8.3

Add $8$ and $12$ .

$\frac{2^{4} \cdot 3^{11}}{2^{20} \cdot 3^{- 3} (2^{6} (3^{- 3}))}$

Step 9

Multiply $2^{20}$ by $2^{6}$ by adding the exponents.

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Step 9.1

Move $2^{6}$ .

$\frac{2^{4} \cdot 3^{11}}{2^{6} \cdot 2^{20} \cdot 3^{- 3} \cdot 3^{- 3}}$

Step 9.2

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

$\frac{2^{4} \cdot 3^{11}}{2^{6 + 20} \cdot 3^{- 3} \cdot 3^{- 3}}$

Step 9.3

Add $6$ and $20$ .

$\frac{2^{4} \cdot 3^{11}}{2^{26} \cdot 3^{- 3} \cdot 3^{- 3}}$

Step 10

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

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Step 10.1

Move $3^{- 3}$ .

$\frac{2^{4} \cdot 3^{11}}{2^{26} \cdot (3^{- 3} \cdot 3^{- 3})}$

Step 10.2

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

$\frac{2^{4} \cdot 3^{11}}{2^{26} \cdot 3^{- 3 - 3}}$

Step 10.3

Subtract $3$ from $- 3$ .

$\frac{2^{4} \cdot 3^{11}}{2^{26} \cdot 3^{- 6}}$

Step 11

Move $3^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2^{4} \cdot 3^{11} \cdot 3^{6}}{2^{26}}$

Step 12

Multiply $3^{11}$ by $3^{6}$ by adding the exponents.

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Step 12.1

Move $3^{6}$ .

$\frac{2^{4} \cdot (3^{6} \cdot 3^{11})}{2^{26}}$

Step 12.2

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

$\frac{2^{4} \cdot 3^{6 + 11}}{2^{26}}$

Step 12.3

Add $6$ and $11$ .

$\frac{2^{4} \cdot 3^{17}}{2^{26}}$

Step 13

Cancel the common factor of $2^{4}$ and $2^{26}$ .

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Step 13.1

Factor $2^{4}$ out of $2^{4} \cdot 3^{17}$ .

$\frac{2^{4} (3^{17})}{2^{26}}$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $2^{4}$ out of $2^{26}$ .

$\frac{2^{4} (3^{17})}{2^{4} \cdot 2^{22}}$

Step 13.2.2

Cancel the common factor.

$\frac{2^{4} \cdot 3^{17}}{2^{4} \cdot 2^{22}}$

Step 13.2.3

Rewrite the expression.

$\frac{3^{17}}{2^{22}}$

Step 14

Evaluate the exponents.

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Step 14.1

Raise $3$ to the power of $17$ .

$\frac{129140163}{2^{22}}$

Step 14.2

Raise $2$ to the power of $22$ .

$\frac{129140163}{4194304}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{129140163}{4194304}$

Decimal Form:

$30.78941416 \dots$

Mixed Number Form:

$30 \frac{3311043}{4194304}$