Basic Math Examples

${(\frac{2 (6.67 \times 10^{- 11}) (8.68 \times 10^{25})}{(25.559 \times 10^{6})})}^{\frac{1}{2}}$

Step 1

Multiply $2$ by $6.67$ .

${(\frac{13.34 \cdot 10^{- 11} \cdot 8.68 \cdot 10^{25}}{25.559 \cdot 10^{6}})}^{\frac{1}{2}}$

Step 2

Multiply $13.34$ by $8.68$ .

${(\frac{115.7912 (10^{- 11} \cdot 10^{25})}{25.559 \cdot 10^{6}})}^{\frac{1}{2}}$

Step 3

Multiply $10^{- 11}$ by $10^{25}$ 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.

${(\frac{115.7912 \cdot 10^{- 11 + 25}}{25.559 \cdot 10^{6}})}^{\frac{1}{2}}$

Step 3.2

Add $- 11$ and $25$ .

${(\frac{115.7912 \cdot 10^{14}}{25.559 \cdot 10^{6}})}^{\frac{1}{2}}$

Step 4

Divide using scientific notation.

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Step 4.1

Group coefficients together and exponents together to divide numbers in scientific notation.

${((\frac{115.7912}{25.559}) (\frac{10^{14}}{10^{6}}))}^{\frac{1}{2}}$

Step 4.2

Divide $115.7912$ by $25.559$ .

${(4.53034938 \frac{10^{14}}{10^{6}})}^{\frac{1}{2}}$

Step 4.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

${(4.53034938 \cdot 10^{14 + 6 \cdot - 1})}^{\frac{1}{2}}$

Step 4.4

Multiply $6$ by $- 1$ .

${(4.53034938 \cdot 10^{14 - 6})}^{\frac{1}{2}}$

Step 4.5

Subtract $6$ from $14$ .

${(4.53034938 \cdot 10^{8})}^{\frac{1}{2}}$

Step 5

Simplify the expression.

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Step 5.1

Apply the product rule to $4.53034938 \cdot 10^{8}$ .

${4.53034938}^{\frac{1}{2}} \cdot {(10^{8})}^{\frac{1}{2}}$

Step 5.2

Rewrite $4.53034938$ as ${2.12846174}^{2}$ .

${({2.12846174}^{2})}^{\frac{1}{2}} \cdot {(10^{8})}^{\frac{1}{2}}$

Step 5.3

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

${2.12846174}^{2 (\frac{1}{2})} \cdot {(10^{8})}^{\frac{1}{2}}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

${2.12846174}^{2 (\frac{1}{2})} \cdot {(10^{8})}^{\frac{1}{2}}$

Step 6.2

Rewrite the expression.

${2.12846174}^{1} \cdot {(10^{8})}^{\frac{1}{2}}$

Step 7

Evaluate the exponent.

$2.12846174 \cdot {(10^{8})}^{\frac{1}{2}}$

Step 8

Multiply the exponents in ${(10^{8})}^{\frac{1}{2}}$ .

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Step 8.1

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

$2.12846174 \cdot 10^{8 (\frac{1}{2})}$

Step 8.2

Cancel the common factor of $2$ .

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Step 8.2.1

Factor $2$ out of $8$ .

$2.12846174 \cdot 10^{2 (4) \frac{1}{2}}$

Step 8.2.2

Cancel the common factor.

$2.12846174 \cdot 10^{2 \cdot 4 \frac{1}{2}}$

Step 8.2.3

Rewrite the expression.

$2.12846174 \cdot 10^{4}$

Step 9

The result can be shown in multiple forms.

Scientific Notation:

$2.12846174 \cdot 10^{4}$

Expanded Form:

$21284.61742125$