Algebra Examples

$\sqrt{9} = 9^{\frac{1}{2}}$

Step 1

Move all terms not containing a variable to the right side of the equation.

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Step 1.1

Subtract $\sqrt{9}$ from both sides of the equation.

$0 = 9^{\frac{1}{2}} - \sqrt{9}$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite $9$ as $3^{2}$ .

$0 = {(3^{2})}^{\frac{1}{2}} - \sqrt{9}$

Step 1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$0 = 3^{2 (\frac{1}{2})} - \sqrt{9}$

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Cancel the common factor.

$0 = 3^{2 (\frac{1}{2})} - \sqrt{9}$

Step 1.2.3.2

Rewrite the expression.

$0 = 3^{1} - \sqrt{9}$

Step 1.2.4

Evaluate the exponent.

$0 = 3 - \sqrt{9}$

Step 1.2.5

Rewrite $9$ as $3^{2}$ .

$0 = 3 - \sqrt{3^{2}}$

Step 1.2.6

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

$0 = 3 - 1 \cdot 3$

Step 1.2.7

Multiply $- 1$ by $3$ .

$0 = 3 - 3$

Step 1.3

Subtract $3$ from $3$ .

$0 = 0$

Step 2

Since $0 = 0$ , the equation will always be true.

Always true