Basic Math Examples

$- 10 a^{6} \div (- 30^{9}) + 20 a^{7}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{- 10 a^{6}}{- 30^{9}} + 20 a^{7}$

Step 1.2

Raise $30$ to the power of $9$ .

$\frac{- 10 a^{6}}{- 1 \cdot 19683000000000} + 20 a^{7}$

Step 1.3

Multiply $- 1$ by $19683000000000$ .

$\frac{- 10 a^{6}}{- 19683000000000} + 20 a^{7}$

Step 1.4

Cancel the common factor of $- 10$ and $- 19683000000000$ .

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Step 1.4.1

Factor $- 10$ out of $- 10 a^{6}$ .

$\frac{- 10 (a^{6})}{- 19683000000000} + 20 a^{7}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $- 10$ out of $- 19683000000000$ .

$\frac{- 10 (a^{6})}{- 10 (1968300000000)} + 20 a^{7}$

Step 1.4.2.2

Cancel the common factor.

$\frac{- 10 a^{6}}{- 10 \cdot 1968300000000} + 20 a^{7}$

Step 1.4.2.3

Rewrite the expression.

$\frac{a^{6}}{1968300000000} + 20 a^{7}$

Step 2

To write $20 a^{7}$ as a fraction with a common denominator, multiply by $\frac{1968300000000}{1968300000000}$ .

$\frac{a^{6}}{1968300000000} + 20 a^{7} \cdot \frac{1968300000000}{1968300000000}$

Step 3

Simplify terms.

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Step 3.1

Combine $20 a^{7}$ and $\frac{1968300000000}{1968300000000}$ .

$\frac{a^{6}}{1968300000000} + \frac{20 a^{7} \cdot 1968300000000}{1968300000000}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{a^{6} + 20 a^{7} \cdot 1968300000000}{1968300000000}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $a^{6}$ out of $a^{6} + 20 a^{7} \cdot 1968300000000$ .

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Step 4.1.1

Multiply by $1$ .

$\frac{a^{6} \cdot 1 + 20 a^{7} \cdot 1968300000000}{1968300000000}$

Step 4.1.2

Factor $a^{6}$ out of $20 a^{7} \cdot 1968300000000$ .

$\frac{a^{6} \cdot 1 + a^{6} (20 a \cdot 1968300000000)}{1968300000000}$

Step 4.1.3

Factor $a^{6}$ out of $a^{6} \cdot 1 + a^{6} (20 a \cdot 1968300000000)$ .

$\frac{a^{6} (1 + 20 a \cdot 1968300000000)}{1968300000000}$

Step 4.2

Multiply $1968300000000$ by $20$ .

$\frac{a^{6} (1 + 39366000000000 a)}{1968300000000}$