Simplify -2x^2(-3x^(1/2)+5)

$- 2 x^{2} (- 3 x^{\frac{1}{2}} + 5)$

Simplify by multiplying through.

Apply the distributive property.

$- 2 x^{2} (- 3 x^{\frac{1}{2}}) - 2 x^{2} \cdot 5$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 3 x^{2} x^{\frac{1}{2}} - 2 x^{2} \cdot 5$

Multiply $5$ by $- 2$ .

$- 2 \cdot - 3 x^{2} x^{\frac{1}{2}} - 10 x^{2}$

Simplify each term.

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

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

$- 2 \cdot - 3 (x^{\frac{1}{2}} x^{2}) - 10 x^{2}$

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

$- 2 \cdot - 3 x^{\frac{1}{2} + 2} - 10 x^{2}$

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

$- 2 \cdot - 3 x^{\frac{1}{2} + 2 \cdot \frac{2}{2}} - 10 x^{2}$

Combine $2$ and $\frac{2}{2}$ .

$- 2 \cdot - 3 x^{\frac{1}{2} + \frac{2 \cdot 2}{2}} - 10 x^{2}$

Combine the numerators over the common denominator.

$- 2 \cdot - 3 x^{\frac{1 + 2 \cdot 2}{2}} - 10 x^{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- 2 \cdot - 3 x^{\frac{1 + 4}{2}} - 10 x^{2}$

Add $1$ and $4$ .

$- 2 \cdot - 3 x^{\frac{5}{2}} - 10 x^{2}$

Multiply $- 2$ by $- 3$ .

$6 x^{\frac{5}{2}} - 10 x^{2}$