Finite Math Examples

$3 x^{\frac{5}{4}} + 4 x^{\frac{1}{4}} (5 x + 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x^{\frac{5}{4}} + 4 x^{\frac{1}{4}} (5 x) + 4 x^{\frac{1}{4}} \cdot 3$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{\frac{1}{4}} x + 4 x^{\frac{1}{4}} \cdot 3$

Step 1.3

Multiply $3$ by $4$ .

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{\frac{1}{4}} x + 12 x^{\frac{1}{4}}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x$ .

$3 x^{\frac{5}{4}} + 4 \cdot 5 (x \cdot x^{\frac{1}{4}}) + 12 x^{\frac{1}{4}}$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$3 x^{\frac{5}{4}} + 4 \cdot 5 (x^{1} x^{\frac{1}{4}}) + 12 x^{\frac{1}{4}}$

Step 1.4.1.2.2

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

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{1 + \frac{1}{4}} + 12 x^{\frac{1}{4}}$

Step 1.4.1.3

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

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{\frac{4}{4} + \frac{1}{4}} + 12 x^{\frac{1}{4}}$

Step 1.4.1.4

Combine the numerators over the common denominator.

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{\frac{4 + 1}{4}} + 12 x^{\frac{1}{4}}$

Step 1.4.1.5

Add $4$ and $1$ .

$3 x^{\frac{5}{4}} + 4 \cdot 5 x^{\frac{5}{4}} + 12 x^{\frac{1}{4}}$

Step 1.4.2

Multiply $4$ by $5$ .

$3 x^{\frac{5}{4}} + 20 x^{\frac{5}{4}} + 12 x^{\frac{1}{4}}$

Step 2

Add $3 x^{\frac{5}{4}}$ and $20 x^{\frac{5}{4}}$ .

$23 x^{\frac{5}{4}} + 12 x^{\frac{1}{4}}$