Algebra Examples

$x^{\frac{5}{11}} x^{\frac{1}{2}}$

Step 1

Multiply $x^{\frac{5}{11}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 1.1

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

$x^{\frac{5}{11} + \frac{1}{2}}$

Step 1.2

To write $\frac{5}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{5}{11} \cdot \frac{2}{2} + \frac{1}{2}}$

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x^{\frac{5}{11} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{11}{11}}$

Step 1.4

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{5}{11}$ by $\frac{2}{2}$ .

$x^{\frac{5 \cdot 2}{11 \cdot 2} + \frac{1}{2} \cdot \frac{11}{11}}$

Step 1.4.2

Multiply $11$ by $2$ .

$x^{\frac{5 \cdot 2}{22} + \frac{1}{2} \cdot \frac{11}{11}}$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{11}{11}$ .

$x^{\frac{5 \cdot 2}{22} + \frac{11}{2 \cdot 11}}$

Step 1.4.4

Multiply $2$ by $11$ .

$x^{\frac{5 \cdot 2}{22} + \frac{11}{22}}$

Step 1.5

Combine the numerators over the common denominator.

$x^{\frac{5 \cdot 2 + 11}{22}}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $5$ by $2$ .

$x^{\frac{10 + 11}{22}}$

Step 1.6.2

Add $10$ and $11$ .

$x^{\frac{21}{22}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[22]{x^{21}}$