Algebra Examples

$\frac{3 {(a^{6} b^{- 4} c)}^{0}}{- 6 {(a^{4} b^{3} c^{4})}^{0}}$

Step 1

Cancel the common factor of $3$ and $- 6$ .

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Step 1.1

Factor $3$ out of $3 {(a^{6} b^{- 4} c)}^{0}$ .

$\frac{3 ({(a^{6} b^{- 4} c)}^{0})}{- 6 {(a^{4} b^{3} c^{4})}^{0}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $- 6 {(a^{4} b^{3} c^{4})}^{0}$ .

$\frac{3 ({(a^{6} b^{- 4} c)}^{0})}{3 (- 2 {(a^{4} b^{3} c^{4})}^{0})}$

Step 1.2.2

Cancel the common factor.

$\frac{3 {(a^{6} b^{- 4} c)}^{0}}{3 (- 2 {(a^{4} b^{3} c^{4})}^{0})}$

Step 1.2.3

Rewrite the expression.

$\frac{{(a^{6} b^{- 4} c)}^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $a^{6} b^{- 4} c$ .

$\frac{{(a^{6} b^{- 4})}^{0} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(a^{6} \frac{1}{b^{4}})}^{0} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.3

Combine $a^{6}$ and $\frac{1}{b^{4}}$ .

$\frac{{(\frac{a^{6}}{b^{4}})}^{0} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.4

Apply the product rule to $\frac{a^{6}}{b^{4}}$ .

$\frac{\frac{{(a^{6})}^{0}}{{(b^{4})}^{0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply the exponents in ${(a^{6})}^{0}$ .

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Step 2.5.1.1

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

$\frac{\frac{a^{6 \cdot 0}}{{(b^{4})}^{0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.5.1.2

Multiply $6$ by $0$ .

$\frac{\frac{a^{0}}{{(b^{4})}^{0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.5.2

Anything raised to $0$ is $1$ .

$\frac{\frac{1}{{(b^{4})}^{0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.6

Simplify the denominator.

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Step 2.6.1

Multiply the exponents in ${(b^{4})}^{0}$ .

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Step 2.6.1.1

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

$\frac{\frac{1}{b^{4 \cdot 0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.6.1.2

Multiply $4$ by $0$ .

$\frac{\frac{1}{b^{0}} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.6.2

Anything raised to $0$ is $1$ .

$\frac{\frac{1}{1} c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.7

Divide $1$ by $1$ .

$\frac{1 c^{0}}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.8

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 2.9

Multiply $1$ by $1$ .

$\frac{1}{- 2 {(a^{4} b^{3} c^{4})}^{0}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $a^{4} b^{3} c^{4}$ .

$\frac{1}{- 2 {(a^{4} b^{3})}^{0} {(c^{4})}^{0}}$

Step 3.2

Apply the product rule to $a^{4} b^{3}$ .

$\frac{1}{- 2 ({(a^{4})}^{0} {(b^{3})}^{0}) {(c^{4})}^{0}}$

Step 3.3

Multiply the exponents in ${(a^{4})}^{0}$ .

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Step 3.3.1

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

$\frac{1}{- 2 (a^{4 \cdot 0} {(b^{3})}^{0}) {(c^{4})}^{0}}$

Step 3.3.2

Multiply $4$ by $0$ .

$\frac{1}{- 2 (a^{0} {(b^{3})}^{0}) {(c^{4})}^{0}}$

Step 3.4

Anything raised to $0$ is $1$ .

$\frac{1}{- 2 (1 {(b^{3})}^{0}) {(c^{4})}^{0}}$

Step 3.5

Multiply ${(b^{3})}^{0}$ by $1$ .

$\frac{1}{- 2 {(b^{3})}^{0} {(c^{4})}^{0}}$

Step 3.6

Multiply the exponents in ${(b^{3})}^{0}$ .

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Step 3.6.1

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

$\frac{1}{- 2 b^{3 \cdot 0} {(c^{4})}^{0}}$

Step 3.6.2

Multiply $3$ by $0$ .

$\frac{1}{- 2 b^{0} {(c^{4})}^{0}}$

Step 3.7

Anything raised to $0$ is $1$ .

$\frac{1}{- 2 \cdot 1 {(c^{4})}^{0}}$

Step 3.8

Multiply the exponents in ${(c^{4})}^{0}$ .

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Step 3.8.1

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

$\frac{1}{- 2 \cdot 1 c^{4 \cdot 0}}$

Step 3.8.2

Multiply $4$ by $0$ .

$\frac{1}{- 2 \cdot 1 c^{0}}$

Step 3.9

Anything raised to $0$ is $1$ .

$\frac{1}{- 2 \cdot 1 \cdot 1}$

Step 3.10

Combine exponents.

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Step 3.10.1

Multiply $- 2$ by $1$ .

$\frac{1}{- 2 \cdot 1}$

Step 3.10.2

Multiply $- 2$ by $1$ .

$\frac{1}{- 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$