Pre-Algebra Examples

$3^{2} \cdot 9^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 3^{2} \cdot 9^{2}$ .

$c^{2} = 3^{2} \cdot 9^{2}$

Step 2

Raise $3$ to the power of $2$ .

$c^{2} = 9 \cdot 9^{2}$

Step 3

Multiply $9$ by $9^{2}$ by adding the exponents.

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Step 3.1

Multiply $9$ by $9^{2}$ .

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Step 3.1.1

Raise $9$ to the power of $1$ .

$c^{2} = 9^{1} \cdot 9^{2}$

Step 3.1.2

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

$c^{2} = 9^{1 + 2}$

Step 3.2

Add $1$ and $2$ .

$c^{2} = 9^{3}$

Step 4

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

$c = \pm \sqrt{9^{3}}$

Step 5

Simplify $\pm \sqrt{9^{3}}$ .

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Step 5.1

Raise $9$ to the power of $3$ .

$c = \pm \sqrt{729}$

Step 5.2

Rewrite $729$ as $27^{2}$ .

$c = \pm \sqrt{27^{2}}$

Step 5.3

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

$c = \pm 27$

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.

$c = 27$

Step 6.2

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

$c = - 27$

Step 6.3

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

$c = 27, - 27$