Basic Math Examples

$\frac{- 30 a^{14} b^{8}}{{(12 a^{3} - b^{- 5})}^{0}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{- 30 a^{14} b^{8}}{{(12 a^{3} - \frac{1}{b^{5}})}^{0}}$

Step 1.2

To write $12 a^{3}$ as a fraction with a common denominator, multiply by $\frac{b^{5}}{b^{5}}$ .

$\frac{- 30 a^{14} b^{8}}{{(\frac{12 a^{3} b^{5}}{b^{5}} - \frac{1}{b^{5}})}^{0}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{- 30 a^{14} b^{8}}{{(\frac{12 a^{3} b^{5} - 1}{b^{5}})}^{0}}$

Step 1.4

Apply the product rule to $\frac{12 a^{3} b^{5} - 1}{b^{5}}$ .

$\frac{- 30 a^{14} b^{8}}{\frac{{(12 a^{3} b^{5} - 1)}^{0}}{{(b^{5})}^{0}}}$

Step 1.5

Simplify the denominator.

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Step 1.5.1

Multiply the exponents in ${(b^{5})}^{0}$ .

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Step 1.5.1.1

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

$\frac{- 30 a^{14} b^{8}}{\frac{{(12 a^{3} b^{5} - 1)}^{0}}{b^{5 \cdot 0}}}$

Step 1.5.1.2

Multiply $5$ by $0$ .

$\frac{- 30 a^{14} b^{8}}{\frac{{(12 a^{3} b^{5} - 1)}^{0}}{b^{0}}}$

Step 1.5.2

Anything raised to $0$ is $1$ .

$\frac{- 30 a^{14} b^{8}}{\frac{{(12 a^{3} b^{5} - 1)}^{0}}{1}}$

Step 1.6

Divide ${(12 a^{3} b^{5} - 1)}^{0}$ by $1$ .

$\frac{- 30 a^{14} b^{8}}{{(12 a^{3} b^{5} - 1)}^{0}}$

Step 1.7

Anything raised to $0$ is $1$ .

$\frac{- 30 a^{14} b^{8}}{1}$

Step 2

Divide $- 30 a^{14} b^{8}$ by $1$ .

$- 30 a^{14} b^{8}$