Algebra Examples

$7.3 \cdot 10^{- 11} = \frac{k^{2}}{0.35}$

Step 1

Rewrite the equation as $\frac{k^{2}}{0.35} = 7.3 \cdot 10^{- 11}$ .

$\frac{k^{2}}{0.35} = 7.3 \cdot 10^{- 11}$

Step 2

Multiply both sides of the equation by $0.35$ .

$0.35 \frac{k^{2}}{0.35} = 0.35 \cdot 7.3 \cdot 10^{- 11}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $0.35$ .

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Step 3.1.1.1

Cancel the common factor.

$0.35 \frac{k^{2}}{0.35} = 0.35 \cdot 7.3 \cdot 10^{- 11}$

Step 3.1.1.2

Rewrite the expression.

$k^{2} = 0.35 \cdot 7.3 \cdot 10^{- 11}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $0.35$ by $7.3$ .

$k^{2} = 2.555 \cdot 10^{- 11}$

Step 4

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

$k = \pm \sqrt{2.555 \cdot 10^{- 11}}$

Step 5

Simplify $\pm \sqrt{2.555 \cdot 10^{- 11}}$ .

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Step 5.1

Rewrite $2.555 \cdot 10^{- 11}$ as $0.2555 \cdot 10^{- 10}$ .

$k = \pm \sqrt{0.2555 \cdot 10^{- 10}}$

Step 5.2

Rewrite $\sqrt{0.2555 \cdot 10^{- 10}}$ as $\sqrt{0.2555} \cdot \sqrt{10^{- 10}}$ .

$k = \pm \sqrt{0.2555} \cdot \sqrt{10^{- 10}}$

Step 5.3

Evaluate the root.

$k = \pm 0.50547007 \cdot \sqrt{10^{- 10}}$

Step 5.4

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

$k = \pm 0.50547007 \cdot \sqrt{{(10^{- 5})}^{2}}$

Step 5.5

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

$k = \pm 0.50547007 \cdot 10^{- 5}$

Step 5.6

Move the decimal point in $0.50547007$ to the right by $1$ place and decrease the power of $10^{- 5}$ by $1$ .

$k = \pm 5.05470078 \cdot 10^{- 6}$

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.

$k = 5.05470078 \cdot 10^{- 6}$

Step 6.2

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

$k = - 5.05470078 \cdot 10^{- 6}$

Step 6.3

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

$k = 5.05470078 \cdot 10^{- 6}, - 5.05470078 \cdot 10^{- 6}$