Calculus Examples

$\frac{{(1.66 \cdot 10^{- 14})}^{2}}{1.8 \cdot 10^{- 5}}$

Step 1

Move $10^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(1.66 \cdot 10^{- 14})}^{2} \cdot 10^{5}}{1.8}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $1.66 \cdot 10^{- 14}$ .

$\frac{{1.66}^{2} \cdot {(10^{- 14})}^{2} \cdot 10^{5}}{1.8}$

Step 2.2

Raise $1.66$ to the power of $2$ .

$\frac{2.7556 \cdot {(10^{- 14})}^{2} \cdot 10^{5}}{1.8}$

Step 2.3

Multiply the exponents in ${(10^{- 14})}^{2}$ .

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Step 2.3.1

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

$\frac{2.7556 \cdot 10^{- 14 \cdot 2} \cdot 10^{5}}{1.8}$

Step 2.3.2

Multiply $- 14$ by $2$ .

$\frac{2.7556 \cdot 10^{- 28} \cdot 10^{5}}{1.8}$

Step 2.4

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

$\frac{2.7556 \cdot \frac{1}{10^{28}} \cdot 10^{5}}{1.8}$

Step 2.5

Raise $10$ to the power of $28$ .

$\frac{2.7556 \cdot \frac{1}{10000000000000000000000000000} \cdot 10^{5}}{1.8}$

Step 2.6

Raise $10$ to the power of $5$ .

$\frac{2.7556 \cdot \frac{1}{10000000000000000000000000000} \cdot 100000}{1.8}$

Step 2.7

Combine exponents.

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Step 2.7.1

Combine $2.7556$ and $\frac{1}{10000000000000000000000000000}$ .

$\frac{\frac{2.7556}{10000000000000000000000000000} \cdot 100000}{1.8}$

Step 2.7.2

Combine $\frac{2.7556}{10000000000000000000000000000}$ and $100000$ .

$\frac{\frac{2.7556 \cdot 100000}{10000000000000000000000000000}}{1.8}$

Step 2.7.3

Multiply $2.7556$ by $100000$ .

$\frac{\frac{275560}{10000000000000000000000000000}}{1.8}$

Step 2.8

Cancel the common factor of $275560$ and $10000000000000000000000000000$ .

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Step 2.8.1

Factor $40$ out of $275560$ .

$\frac{\frac{40 (6889)}{10000000000000000000000000000}}{1.8}$

Step 2.8.2

Cancel the common factors.

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Step 2.8.2.1

Factor $40$ out of $10000000000000000000000000000$ .

$\frac{\frac{40 \cdot 6889}{40 \cdot 250000000000000000000000000}}{1.8}$

Step 2.8.2.2

Cancel the common factor.

$\frac{\frac{40 \cdot 6889}{40 \cdot 250000000000000000000000000}}{1.8}$

Step 2.8.2.3

Rewrite the expression.

$\frac{\frac{6889}{250000000000000000000000000}}{1.8}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{6889}{250000000000000000000000000} \cdot \frac{1}{1.8}$

Step 4

Divide $1$ by $1.8$ .

$\frac{6889}{250000000000000000000000000} \cdot 0.\overline{5}$

Step 5

Multiply $\frac{6889}{250000000000000000000000000} \cdot 0.\overline{5}$ .

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Step 5.1

Combine $\frac{6889}{250000000000000000000000000}$ and $0.\overline{5}$ .

$\frac{6889 \cdot 0.\overline{5}}{250000000000000000000000000}$

Step 5.2

Multiply $6889$ by $0.\overline{5}$ .

$\frac{3827.\overline{2}}{250000000000000000000000000}$

Step 6

Divide $3827.\overline{2}$ by $250000000000000000000000000$ .

$0$