Algebra Examples

$x^{2} \cdot x^{\frac{1}{2}}$

Step 1

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

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

Step 2

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

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

Step 3

Combine $2$ and $\frac{2}{2}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

$x^{\frac{4 + 1}{2}}$

Step 5.2

Add $4$ and $1$ .

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