Solve for c 2^2*10^2=c^2

$2^{2} \cdot 10^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 2^{2} \cdot 10^{2}$ .

$c^{2} = 2^{2} \cdot 10^{2}$

Step 2

Raise $2$ to the power of $2$ .

$c^{2} = 4 \cdot 10^{2}$

Step 3

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

$c = \pm \sqrt{4 \cdot 10^{2}}$

Step 4

Simplify $\pm \sqrt{4 \cdot 10^{2}}$ .

Rewrite $\sqrt{4 \cdot 10^{2}}$ as $\sqrt{4} \cdot \sqrt{10^{2}}$ .

$c = \pm \sqrt{4} \cdot \sqrt{10^{2}}$

Evaluate the root.

$c = \pm 2 \cdot \sqrt{10^{2}}$

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

$c = \pm 2 \cdot 10$

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

$c = \pm 2 \cdot 10^{1}$

Step 5

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

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

$c = 2 \cdot 10^{1}$

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

$c = - 2 \cdot 10^{1}$

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

$c = 2 \cdot 10^{1}, - 2 \cdot 10^{1}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$c = 2 \cdot 10^{1}, - 2 \cdot 10^{1}$

Expanded Form:

$c = 20, - 20$