Simplify (4x)(9x^(1/2))

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

Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $2$ .

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

Multiply $4$ by $9$ .

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