Evaluate 2d+ cube root of -45d

$2 d + \sqrt[3]{- 45 d}$

Step 1

Rewrite $- 45 d$ as ${({(- 1)}^{3})}^{3} \cdot (45 d)$ .

Rewrite $- 45$ as $- 1 (45)$ .

$2 d + \sqrt[3]{- 1 (45) d}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$2 d + \sqrt[3]{{(- 1)}^{3} \cdot 45 d}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$2 d + \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot 45 d}$

Add parentheses.

$2 d + \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (45 d)}$

Step 2

Pull terms out from under the radical.

$2 d + {(- 1)}^{3} \sqrt[3]{45 d}$

Step 3

Raise $- 1$ to the power of $3$ .

$2 d - 1 \sqrt[3]{45 d}$

Step 4

Rewrite $- 1 \sqrt[3]{45 d}$ as $- \sqrt[3]{45 d}$ .

$2 d - \sqrt[3]{45 d}$