Precalculus Examples

$x^{\frac{1}{4}} (2 x^{\frac{3}{4}} - x^{\frac{1}{4}})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$x^{\frac{1}{4}} (2 x^{\frac{3}{4}}) + x^{\frac{1}{4}} (- x^{\frac{1}{4}})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 x^{\frac{1}{4}} x^{\frac{3}{4}} + x^{\frac{1}{4}} (- x^{\frac{1}{4}})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$2 x^{\frac{1}{4}} x^{\frac{3}{4}} - x^{\frac{1}{4}} x^{\frac{1}{4}}$

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{\frac{1}{4}}$ by $x^{\frac{3}{4}}$ by adding the exponents.

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Step 2.1.1

Move $x^{\frac{3}{4}}$ .

$2 (x^{\frac{3}{4}} x^{\frac{1}{4}}) - x^{\frac{1}{4}} x^{\frac{1}{4}}$

Step 2.1.2

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

$2 x^{\frac{3}{4} + \frac{1}{4}} - x^{\frac{1}{4}} x^{\frac{1}{4}}$

Step 2.1.3

Combine the numerators over the common denominator.

$2 x^{\frac{3 + 1}{4}} - x^{\frac{1}{4}} x^{\frac{1}{4}}$

Step 2.1.4

Add $3$ and $1$ .

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

Step 2.1.5

Divide $4$ by $4$ .

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

Step 2.2

Simplify $2 x^{1}$ .

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

Step 2.3

Multiply $x^{\frac{1}{4}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

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Step 2.3.1

Move $x^{\frac{1}{4}}$ .

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

Step 2.3.2

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

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

Step 2.3.3

Combine the numerators over the common denominator.

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

Step 2.3.4

Add $1$ and $1$ .

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

Step 2.3.5

Cancel the common factor of $2$ and $4$ .

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Step 2.3.5.1

Factor $2$ out of $2$ .

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

Step 2.3.5.2

Cancel the common factors.

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Step 2.3.5.2.1

Factor $2$ out of $4$ .

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

Step 2.3.5.2.2

Cancel the common factor.

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

Step 2.3.5.2.3

Rewrite the expression.

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