Algebra Examples

$4 x^{\frac{5}{4}} \cdot 2 x^{\frac{1}{2}}$

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x^{\frac{5}{4}} x^{\frac{1}{2}}$

Step 2

Multiply $x^{\frac{5}{4}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

$4 \cdot 2 (x^{\frac{1}{2}} x^{\frac{5}{4}})$

Step 2.2

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

$4 \cdot 2 x^{\frac{1}{2} + \frac{5}{4}}$

Step 2.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot 2 x^{\frac{1}{2} \cdot \frac{2}{2} + \frac{5}{4}}$

Step 2.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$4 \cdot 2 x^{\frac{2}{2 \cdot 2} + \frac{5}{4}}$

Step 2.4.2

Multiply $2$ by $2$ .

$4 \cdot 2 x^{\frac{2}{4} + \frac{5}{4}}$

Step 2.5

Combine the numerators over the common denominator.

$4 \cdot 2 x^{\frac{2 + 5}{4}}$

Step 2.6

Add $2$ and $5$ .

$4 \cdot 2 x^{\frac{7}{4}}$

Step 3

Multiply $4$ by $2$ .

$8 x^{\frac{7}{4}}$