Algebra Examples

$(4 x) (9 x^{\frac{1}{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot 9 x \cdot x^{\frac{1}{2}}$

Step 2

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

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Step 2.1

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

$4 \cdot 9 (x^{\frac{1}{2}} x)$

Step 2.2

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

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Step 2.2.1

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

$4 \cdot 9 (x^{\frac{1}{2}} x^{1})$

Step 2.2.2

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

$4 \cdot 9 x^{\frac{1}{2} + 1}$

Step 2.3

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

$4 \cdot 9 x^{\frac{1}{2} + \frac{2}{2}}$

Step 2.4

Combine the numerators over the common denominator.

$4 \cdot 9 x^{\frac{1 + 2}{2}}$

Step 2.5

Add $1$ and $2$ .

$4 \cdot 9 x^{\frac{3}{2}}$

Step 3

Multiply $4$ by $9$ .

$36 x^{\frac{3}{2}}$