Algebra Examples

$\frac{(64 a^{3} b^{4} c^{- 5}) (32 a^{4} b^{3} c^{5})}{(256 a^{9} b^{6} c^{- 5})}$

Step 1

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

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Step 1.1

Move $a^{4}$ .

$\frac{64 (a^{4} a^{3}) b^{4} c^{- 5} (32 b^{3} c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 1.2

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

$\frac{64 a^{4 + 3} b^{4} c^{- 5} (32 b^{3} c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 1.3

Add $4$ and $3$ .

$\frac{64 a^{7} b^{4} c^{- 5} (32 b^{3} c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 2

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

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Step 2.1

Move $b^{3}$ .

$\frac{64 a^{7} (b^{3} b^{4}) c^{- 5} (32 c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 2.2

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

$\frac{64 a^{7} b^{3 + 4} c^{- 5} (32 c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 2.3

Add $3$ and $4$ .

$\frac{64 a^{7} b^{7} c^{- 5} (32 c^{5})}{256 a^{9} b^{6} c^{- 5}}$

Step 3

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

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Step 3.1

Move $c^{5}$ .

$\frac{64 a^{7} b^{7} (c^{5} c^{- 5}) \cdot 32}{256 a^{9} b^{6} c^{- 5}}$

Step 3.2

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

$\frac{64 a^{7} b^{7} c^{5 - 5} \cdot 32}{256 a^{9} b^{6} c^{- 5}}$

Step 3.3

Subtract $5$ from $5$ .

$\frac{64 a^{7} b^{7} c^{0} \cdot 32}{256 a^{9} b^{6} c^{- 5}}$

Step 4

Simplify.

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Step 4.1

Simplify $64 a^{7} b^{7} c^{0} \cdot 32$ .

$\frac{64 a^{7} b^{7} \cdot 32}{256 a^{9} b^{6} c^{- 5}}$

Step 4.2

Move $c^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{64 a^{7} b^{7} \cdot 32 c^{5}}{256 a^{9} b^{6}}$

Step 5

Cancel the common factor of $64$ and $256$ .

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Step 5.1

Factor $64$ out of $64 a^{7} b^{7} \cdot 32 c^{5}$ .

$\frac{64 (a^{7} b^{7} \cdot 32 c^{5})}{256 a^{9} b^{6}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $64$ out of $256 a^{9} b^{6}$ .

$\frac{64 (a^{7} b^{7} \cdot 32 c^{5})}{64 (4 a^{9} b^{6})}$

Step 5.2.2

Cancel the common factor.

$\frac{64 (a^{7} b^{7} \cdot 32 c^{5})}{64 (4 a^{9} b^{6})}$

Step 5.2.3

Rewrite the expression.

$\frac{a^{7} b^{7} \cdot 32 c^{5}}{4 a^{9} b^{6}}$

Step 6

Cancel the common factor of $a^{7}$ and $a^{9}$ .

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Step 6.1

Factor $a^{7}$ out of $a^{7} b^{7} \cdot 32 c^{5}$ .

$\frac{a^{7} (b^{7} \cdot 32 c^{5})}{4 a^{9} b^{6}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $a^{7}$ out of $4 a^{9} b^{6}$ .

$\frac{a^{7} (b^{7} \cdot 32 c^{5})}{a^{7} (4 a^{2} b^{6})}$

Step 6.2.2

Cancel the common factor.

$\frac{a^{7} (b^{7} \cdot 32 c^{5})}{a^{7} (4 a^{2} b^{6})}$

Step 6.2.3

Rewrite the expression.

$\frac{b^{7} \cdot 32 c^{5}}{4 a^{2} b^{6}}$

Step 7

Cancel the common factor of $b^{7}$ and $b^{6}$ .

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Step 7.1

Factor $b^{6}$ out of $b^{7} \cdot 32 c^{5}$ .

$\frac{b^{6} (b \cdot 32 c^{5})}{4 a^{2} b^{6}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $b^{6}$ out of $4 a^{2} b^{6}$ .

$\frac{b^{6} (b \cdot 32 c^{5})}{b^{6} (4 a^{2})}$

Step 7.2.2

Cancel the common factor.

$\frac{b^{6} (b \cdot 32 c^{5})}{b^{6} (4 a^{2})}$

Step 7.2.3

Rewrite the expression.

$\frac{b \cdot 32 c^{5}}{4 a^{2}}$

Step 8

Cancel the common factor of $32$ and $4$ .

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Step 8.1

Factor $4$ out of $b \cdot 32 c^{5}$ .

$\frac{4 (b \cdot 8 c^{5})}{4 a^{2}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

$\frac{4 (b \cdot 8 c^{5})}{4 (a^{2})}$

Step 8.2.2

Cancel the common factor.

$\frac{4 (b \cdot 8 c^{5})}{4 a^{2}}$

Step 8.2.3

Rewrite the expression.

$\frac{b \cdot 8 c^{5}}{a^{2}}$

Step 9

Move $8$ to the left of $b$ .

$\frac{8 b c^{5}}{a^{2}}$