Precalculus Examples

$x^{- \frac{1}{2}} (x^{\frac{5}{2}} - 2 x^{\frac{3}{2}})$

Step 1

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

$\frac{1}{x^{\frac{1}{2}}} (x^{\frac{5}{2}} - 2 x^{\frac{3}{2}})$

Step 2

Multiply $\frac{1}{x^{\frac{1}{2}}}$ by $x^{\frac{5}{2}} - 2 x^{\frac{3}{2}}$ .

$\frac{x^{\frac{5}{2}} - 2 x^{\frac{3}{2}}}{x^{\frac{1}{2}}}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Factor $x^{\frac{3}{2}}$ out of $x^{\frac{5}{2}} - 2 x^{\frac{3}{2}}$ .

Tap for more steps...

Step 3.1.1

Factor $x^{\frac{3}{2}}$ out of $x^{\frac{5}{2}}$ .

$\frac{x^{\frac{3}{2}} x^{\frac{2}{2}} - 2 x^{\frac{3}{2}}}{x^{\frac{1}{2}}}$

Step 3.1.2

Factor $x^{\frac{3}{2}}$ out of $- 2 x^{\frac{3}{2}}$ .

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

Step 3.1.3

Factor $x^{\frac{3}{2}}$ out of $x^{\frac{3}{2}} x^{\frac{2}{2}} + x^{\frac{3}{2}} \cdot - 2$ .

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

Step 3.2

Divide $2$ by $2$ .

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

Step 3.3

Simplify.

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

Step 4

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 5

Multiply $x^{\frac{3}{2}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $x^{- \frac{1}{2}}$ .

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

Step 5.2

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

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

Step 5.3

Combine the numerators over the common denominator.

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

Step 5.4

Add $- 1$ and $3$ .

$x^{\frac{2}{2}} (x - 2)$

Step 5.5

Divide $2$ by $2$ .

$x^{1} (x - 2)$

Step 6

Simplify $x^{1} (x - 2)$ .

$x (x - 2)$

Step 7

Apply the distributive property.

$x \cdot x + x \cdot - 2$

Step 8

Simplify the expression.

Tap for more steps...

Step 8.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2$

Step 8.2

Move $- 2$ to the left of $x$ .

$x^{2} - 2 x$