Basic Math Examples

$y^{2} = \frac{2.94 \cdot 10^{4}}{6.42 \cdot 10^{- 6}}$

Step 1

Reduce the expression $\frac{2.94 \cdot 10^{4}}{6.42 \cdot 10^{- 6}}$ by cancelling the common factors.

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Step 1.1

Factor $10^{- 6}$ out of $2.94 \cdot 10^{4}$ .

$y^{2} = \frac{10^{- 6} \cdot 2.94 \cdot 10^{10}}{6.42 \cdot 10^{- 6}}$

Step 1.2

Factor $10^{- 6}$ out of $6.42 \cdot 10^{- 6}$ .

$y^{2} = \frac{10^{- 6} \cdot 2.94 \cdot 10^{10}}{10^{- 6} \cdot 6.42}$

Step 1.3

Cancel the common factor.

$y^{2} = \frac{10^{- 6} \cdot 2.94 \cdot 10^{10}}{10^{- 6} \cdot 6.42}$

Step 1.4

Rewrite the expression.

$y^{2} = \frac{2.94 \cdot 10^{10}}{6.42}$

Step 2

Divide using scientific notation.

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Step 2.1

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

$y^{2} = (\frac{2.94}{6.42}) (\frac{10^{10}}{1})$

Step 2.2

Divide $2.94$ by $6.42$ .

$y^{2} = 0.45794392 \frac{10^{10}}{1}$

Step 2.3

Divide $10^{10}$ by $1$ .

$y^{2} = 0.45794392 \cdot 10^{10}$

Step 3

Move the decimal point in $0.45794392$ to the right by $1$ place and decrease the power of $10^{10}$ by $1$ .

$y^{2} = 4.57943925 \cdot 10^{9}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{4.57943925 \cdot 10^{9}}$

Step 5

Simplify $\pm \sqrt{4.57943925 \cdot 10^{9}}$ .

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Step 5.1

Rewrite $4.57943925 \cdot 10^{9}$ as $0.45794392 \cdot 10^{10}$ .

$y = \pm \sqrt{0.45794392 \cdot 10^{10}}$

Step 5.2

Rewrite $\sqrt{0.45794392 \cdot 10^{10}}$ as $\sqrt{0.45794392} \cdot \sqrt{10^{10}}$ .

$y = \pm \sqrt{0.45794392} \cdot \sqrt{10^{10}}$

Step 5.3

Evaluate the root.

$y = \pm 0.67671554 \cdot \sqrt{10^{10}}$

Step 5.4

Rewrite $10^{10}$ as ${(10^{5})}^{2}$ .

$y = \pm 0.67671554 \cdot \sqrt{{(10^{5})}^{2}}$

Step 5.5

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

$y = \pm 0.67671554 \cdot 10^{5}$

Step 5.6

Move the decimal point in $0.67671554$ to the right by $1$ place and decrease the power of $10^{5}$ by $1$ .

$y = \pm 6.76715542 \cdot 10^{4}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 6.76715542 \cdot 10^{4}$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 6.76715542 \cdot 10^{4}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = 6.76715542 \cdot 10^{4}, - 6.76715542 \cdot 10^{4}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$y = 6.76715542 \cdot 10^{4}, - 6.76715542 \cdot 10^{4}$

Expanded Form:

$y = 67671.55423319, - 67671.55423319$