Basic Math Examples

$\sqrt{\frac{(6.67 \times 10^{- 11}) (6 \times 10^{24})}{(1.5 \times 10^{11})}}$

Step 1

Multiply $6.67$ by $6$ .

$\sqrt{\frac{40.02 (10^{- 11} \cdot 10^{24})}{1.5 \cdot 10^{11}}}$

Step 2

Multiply $10^{- 11}$ by $10^{24}$ by adding the exponents.

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Step 2.1

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

$\sqrt{\frac{40.02 \cdot 10^{- 11 + 24}}{1.5 \cdot 10^{11}}}$

Step 2.2

Add $- 11$ and $24$ .

$\sqrt{\frac{40.02 \cdot 10^{13}}{1.5 \cdot 10^{11}}}$

Step 3

Divide using scientific notation.

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Step 3.1

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

$\sqrt{(\frac{40.02}{1.5}) (\frac{10^{13}}{10^{11}})}$

Step 3.2

Divide $40.02$ by $1.5$ .

$\sqrt{26.68 \frac{10^{13}}{10^{11}}}$

Step 3.3

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

$\sqrt{26.68 \cdot 10^{13 + 11 \cdot - 1}}$

Step 3.4

Multiply $11$ by $- 1$ .

$\sqrt{26.68 \cdot 10^{13 - 11}}$

Step 3.5

Subtract $11$ from $13$ .

$\sqrt{26.68 \cdot 10^{2}}$

Step 4

Rewrite $\sqrt{26.68 \cdot 10^{2}}$ as $\sqrt{26.68} \cdot \sqrt{10^{2}}$ .

$\sqrt{26.68} \cdot \sqrt{10^{2}}$

Step 5

Evaluate the root.

$5.16526862 \cdot \sqrt{10^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$5.16526862 \cdot 10$

Step 7

Raise $10$ to the power of $1$ .

$5.16526862 \cdot 10^{1}$

Step 8

The result can be shown in multiple forms.

Scientific Notation:

$5.16526862 \cdot 10^{1}$

Expanded Form:

$51.65268628$