Evaluate -2(5)^(1/3)-5(5)^(1/2)

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

Factor out negative.

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

Raise $5$ to the power of $1$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 14.60029178 \dots$