Algebra Examples

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

Step 1

Subtract $9^{\frac{1}{2}}$ from both sides of the equation.

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

Step 2

Simplify $\sqrt{9} - 9^{\frac{1}{2}}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

Cancel the common factor.

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

Step 2.1.5.2

Rewrite the expression.

$3 - 3^{1} = 0$

Step 2.1.6

Evaluate the exponent.

$3 - 1 \cdot 3 = 0$

Step 2.1.7

Multiply $- 1$ by $3$ .

$3 - 3 = 0$

Step 2.2

Subtract $3$ from $3$ .

$0 = 0$

Step 3

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

Always true