Basic Math Examples

$\frac{{(11^{- 3} - 7^{7})}^{0}}{11^{3} - 7^{6}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{{(\frac{1}{11^{3}} - 7^{7})}^{0}}{11^{3} - 7^{6}}$

Step 1.2

Raise $11$ to the power of $3$ .

$\frac{{(\frac{1}{1331} - 7^{7})}^{0}}{11^{3} - 7^{6}}$

Step 1.3

Raise $7$ to the power of $7$ .

$\frac{{(\frac{1}{1331} - 1 \cdot 823543)}^{0}}{11^{3} - 7^{6}}$

Step 1.4

Multiply $- 1$ by $823543$ .

$\frac{{(\frac{1}{1331} - 823543)}^{0}}{11^{3} - 7^{6}}$

Step 1.5

To write $- 823543$ as a fraction with a common denominator, multiply by $\frac{1331}{1331}$ .

$\frac{{(\frac{1}{1331} - 823543 \cdot \frac{1331}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.6

Combine $- 823543$ and $\frac{1331}{1331}$ .

$\frac{{(\frac{1}{1331} + \frac{- 823543 \cdot 1331}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.7

Combine the numerators over the common denominator.

$\frac{{(\frac{1 - 823543 \cdot 1331}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $- 823543$ by $1331$ .

$\frac{{(\frac{1 - 1096135733}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.8.2

Subtract $1096135733$ from $1$ .

$\frac{{(\frac{- 1096135732}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.9

Move the negative in front of the fraction.

$\frac{{(- \frac{1096135732}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.10

Apply the product rule to $- \frac{1096135732}{1331}$ .

$\frac{{(- 1)}^{0} {(\frac{1096135732}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.11

Anything raised to $0$ is $1$ .

$\frac{1 {(\frac{1096135732}{1331})}^{0}}{11^{3} - 7^{6}}$

Step 1.12

Apply the product rule to $\frac{1096135732}{1331}$ .

$\frac{1 \frac{1096135732^{0}}{1331^{0}}}{11^{3} - 7^{6}}$

Step 1.13

Anything raised to $0$ is $1$ .

$\frac{1 \frac{1}{1331^{0}}}{11^{3} - 7^{6}}$

Step 1.14

Anything raised to $0$ is $1$ .

$\frac{1 (\frac{1}{1})}{11^{3} - 7^{6}}$

Step 1.15

Divide $1$ by $1$ .

$\frac{1 \cdot 1}{11^{3} - 7^{6}}$

Step 1.16

Multiply $1$ by $1$ .

$\frac{1}{11^{3} - 7^{6}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $11$ to the power of $3$ .

$\frac{1}{1331 - 7^{6}}$

Step 2.2

Raise $7$ to the power of $6$ .

$\frac{1}{1331 - 1 \cdot 117649}$

Step 2.3

Multiply $- 1$ by $117649$ .

$\frac{1}{1331 - 117649}$

Step 2.4

Subtract $117649$ from $1331$ .

$\frac{1}{- 116318}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{116318}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{116318}$

Decimal Form:

$- 8.59712168 \cdot 10^{- 6}$