Algebra Examples

$\frac{- 15 a^{0} b c^{2}}{- 60 a^{- 8} b^{- 6} c^{0}}$

Step 1

Simplify.

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Step 1.1

Move $a^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 15 a^{0} b c^{2} a^{8}}{- 60 b^{- 6}}$

Step 1.2

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

$\frac{- 15 a^{0} b c^{2} a^{8} b^{6}}{- 60}$

Step 2

Move $c^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 15 a^{0} b c^{2} a^{8} b^{6} c^{0}}{- 60 c^{0}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $a^{0}$ by $a^{8}$ by adding the exponents.

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Step 3.1.1

Move $a^{8}$ .

$\frac{- 15 (a^{8} a^{0}) b c^{2} b^{6} c^{0}}{- 60 c^{0}}$

Step 3.1.2

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

$\frac{- 15 a^{8 + 0} b c^{2} b^{6} c^{0}}{- 60 c^{0}}$

Step 3.1.3

Add $8$ and $0$ .

$\frac{- 15 a^{8} b c^{2} b^{6} c^{0}}{- 60 c^{0}}$

Step 3.2

Multiply $b$ by $b^{6}$ by adding the exponents.

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Step 3.2.1

Move $b^{6}$ .

$\frac{- 15 a^{8} (b^{6} b) c^{2} c^{0}}{- 60 c^{0}}$

Step 3.2.2

Multiply $b^{6}$ by $b$ .

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Step 3.2.2.1

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

$\frac{- 15 a^{8} (b^{6} b^{1}) c^{2} c^{0}}{- 60 c^{0}}$

Step 3.2.2.2

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

$\frac{- 15 a^{8} b^{6 + 1} c^{2} c^{0}}{- 60 c^{0}}$

Step 3.2.3

Add $6$ and $1$ .

$\frac{- 15 a^{8} b^{7} c^{2} c^{0}}{- 60 c^{0}}$

Step 3.3

Multiply $c^{2}$ by $c^{0}$ by adding the exponents.

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Step 3.3.1

Move $c^{0}$ .

$\frac{- 15 a^{8} b^{7} (c^{0} c^{2})}{- 60 c^{0}}$

Step 3.3.2

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

$\frac{- 15 a^{8} b^{7} c^{0 + 2}}{- 60 c^{0}}$

Step 3.3.3

Add $0$ and $2$ .

$\frac{- 15 a^{8} b^{7} c^{2}}{- 60 c^{0}}$

Step 4

Move $c^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 15 a^{8} b^{7} c^{2} c^{0}}{- 60}$

Step 5

Multiply $c^{2}$ by $c^{0}$ by adding the exponents.

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Step 5.1

Move $c^{0}$ .

$\frac{- 15 a^{8} b^{7} (c^{0} c^{2})}{- 60}$

Step 5.2

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

$\frac{- 15 a^{8} b^{7} c^{0 + 2}}{- 60}$

Step 5.3

Add $0$ and $2$ .

$\frac{- 15 a^{8} b^{7} c^{2}}{- 60}$

Step 6

Cancel the common factor of $- 15$ and $- 60$ .

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Step 6.1

Factor $- 15$ out of $- 15 a^{8} b^{7} c^{2}$ .

$\frac{- 15 (a^{8} b^{7} c^{2})}{- 60}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $- 15$ out of $- 60$ .

$\frac{- 15 (a^{8} b^{7} c^{2})}{- 15 (4)}$

Step 6.2.2

Cancel the common factor.

$\frac{- 15 (a^{8} b^{7} c^{2})}{- 15 \cdot 4}$

Step 6.2.3

Rewrite the expression.

$\frac{a^{8} b^{7} c^{2}}{4}$