Precalculus Examples

$(x) (6 - 4 x^{- \frac{1}{2}})$

Step 1

Simplify each term.

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Step 1.1

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

$x (6 - 4 \frac{1}{x^{\frac{1}{2}}})$

Step 1.2

Combine $- 4$ and $\frac{1}{x^{\frac{1}{2}}}$ .

$x (6 + \frac{- 4}{x^{\frac{1}{2}}})$

Step 1.3

Move the negative in front of the fraction.

$x (6 - \frac{4}{x^{\frac{1}{2}}})$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$x \cdot 6 + x (- \frac{4}{x^{\frac{1}{2}}})$

Step 2.2

Reorder.

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Step 2.2.1

Move $6$ to the left of $x$ .

$6 \cdot x + x (- \frac{4}{x^{\frac{1}{2}}})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$6 \cdot x - x \frac{4}{x^{\frac{1}{2}}}$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{4}{x^{\frac{1}{2}}}$ and $x$ .

$6 x - \frac{4 x}{x^{\frac{1}{2}}}$

Step 3.2

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

$6 x - (4 x \cdot x^{- \frac{1}{2}})$

Step 3.3

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

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Step 3.3.1

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

$6 x - (4 (x^{- \frac{1}{2}} x))$

Step 3.3.2

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

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Step 3.3.2.1

Raise $x$ to the power of $1$ .

$6 x - (4 (x^{- \frac{1}{2}} x^{1}))$

Step 3.3.2.2

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

$6 x - (4 x^{- \frac{1}{2} + 1})$

Step 3.3.3

Write $1$ as a fraction with a common denominator.

$6 x - (4 x^{- \frac{1}{2} + \frac{2}{2}})$

Step 3.3.4

Combine the numerators over the common denominator.

$6 x - (4 x^{\frac{- 1 + 2}{2}})$

Step 3.3.5

Add $- 1$ and $2$ .

$6 x - (4 x^{\frac{1}{2}})$

Step 3.4

Multiply $4$ by $- 1$ .

$6 x - 4 x^{\frac{1}{2}}$