Finite Math Examples

$x = \sqrt{\frac{20 \cdot 10^{- 3}}{5 \cdot 10^{3}}}$

Step 1

Divide using scientific notation.

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Step 1.1

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

$x = \sqrt{(\frac{20}{5}) (\frac{10^{- 3}}{10^{3}})}$

Step 1.2

Divide $20$ by $5$ .

$x = \sqrt{4 \frac{10^{- 3}}{10^{3}}}$

Step 1.3

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

$x = \sqrt{4 \cdot 10^{- 3 + 3 \cdot - 1}}$

Step 1.4

Multiply $3$ by $- 1$ .

$x = \sqrt{4 \cdot 10^{- 3 - 3}}$

Step 1.5

Subtract $3$ from $- 3$ .

$x = \sqrt{4 \cdot 10^{- 6}}$

Step 2

Rewrite $\sqrt{4 \cdot 10^{- 6}}$ as $\sqrt{4} \cdot \sqrt{10^{- 6}}$ .

$x = \sqrt{4} \cdot \sqrt{10^{- 6}}$

Step 3

Evaluate the root.

$x = 2 \cdot \sqrt{10^{- 6}}$

Step 4

Rewrite $10^{- 6}$ as ${(10^{- 3})}^{2}$ .

$x = 2 \cdot \sqrt{{(10^{- 3})}^{2}}$

Step 5

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

$x = 2 \cdot 10^{- 3}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$x = 2 \cdot 10^{- 3}$

Expanded Form:

$x = 0.002$