Calculus Examples

$\frac{(6.67 \cdot 10^{- 11}) (5.97 \cdot 10^{2} \cdot 4)}{{(6.38 \cdot 10^{6})}^{2}}$

Step 1

Multiply $5.97$ by $4$ .

$\frac{6.67 \cdot 10^{- 11} \cdot 23.88 \cdot 10^{2}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 2

Multiply $6.67$ by $23.88$ .

$\frac{159.2796 (10^{- 11} \cdot 10^{2})}{{(6.38 \cdot 10^{6})}^{2}}$

Step 3

Multiply $10^{- 11}$ by $10^{2}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{159.2796 \cdot 10^{- 11 + 2}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 3.2

Add $- 11$ and $2$ .

$\frac{159.2796 \cdot 10^{- 9}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 4

Move $10^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{159.2796}{{(6.38 \cdot 10^{6})}^{2} \cdot 10^{9}}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the product rule to $6.38 \cdot 10^{6}$ .

$\frac{159.2796}{{6.38}^{2} \cdot {(10^{6})}^{2} \cdot 10^{9}}$

Step 5.2

Raise $6.38$ to the power of $2$ .

$\frac{159.2796}{40.7044 \cdot {(10^{6})}^{2} \cdot 10^{9}}$

Step 5.3

Multiply the exponents in ${(10^{6})}^{2}$ .

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Step 5.3.1

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

$\frac{159.2796}{40.7044 \cdot 10^{6 \cdot 2} \cdot 10^{9}}$

Step 5.3.2

Multiply $6$ by $2$ .

$\frac{159.2796}{40.7044 \cdot 10^{12} \cdot 10^{9}}$

Step 5.4

Raise $10$ to the power of $12$ .

$\frac{159.2796}{40.7044 \cdot 1000000000000 \cdot 10^{9}}$

Step 5.5

Raise $10$ to the power of $9$ .

$\frac{159.2796}{40.7044 \cdot 1000000000000 \cdot 1000000000}$

Step 5.6

Combine exponents.

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Step 5.6.1

Multiply $40.7044$ by $1000000000000$ .

$\frac{159.2796}{40704400000000 \cdot 1000000000}$

Step 5.6.2

Multiply $40704400000000$ by $1000000000$ .

$\frac{159.2796}{40704400000000000000000}$

Step 6

Divide $159.2796$ by $40704400000000000000000$ .

$0$