Algebra Examples

$2 \cdot 36^{- \frac{1}{2}} + 6^{- 1}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \cdot \frac{1}{36^{\frac{1}{2}}} + 6^{- 1}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $36$ as $6^{2}$ .

$2 \cdot \frac{1}{{(6^{2})}^{\frac{1}{2}}} + 6^{- 1}$

Step 1.2.2

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

$2 \cdot \frac{1}{6^{2 (\frac{1}{2})}} + 6^{- 1}$

Step 1.2.3

Cancel the common factor of $2$ .

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Step 1.2.3.1

Cancel the common factor.

$2 \cdot \frac{1}{6^{2 (\frac{1}{2})}} + 6^{- 1}$

Step 1.2.3.2

Rewrite the expression.

$2 \cdot \frac{1}{6^{1}} + 6^{- 1}$

Step 1.2.4

Evaluate the exponent.

$2 \cdot \frac{1}{6} + 6^{- 1}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $6$ .

$2 \cdot \frac{1}{2 (3)} + 6^{- 1}$

Step 1.3.2

Cancel the common factor.

$2 \cdot \frac{1}{2 \cdot 3} + 6^{- 1}$

Step 1.3.3

Rewrite the expression.

$\frac{1}{3} + 6^{- 1}$

Step 1.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3} + \frac{1}{6}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{6}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{2}{3 \cdot 2} + \frac{1}{6}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{2}{6} + \frac{1}{6}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{2 + 1}{6}$

Step 4.2

Add $2$ and $1$ .

$\frac{3}{6}$

Step 5

Cancel the common factor of $3$ and $6$ .

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Step 5.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{6}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$