Do not use a calculator. Dll variable bases are positive. 1. Determine: a) \( \sqrt[3]{64} \) c) \( \sqrt[3]{-27} \)

Let's solve each part step by step. ### Part a: \( \sqrt[3]{64} \) To find the cube root of 64, we need to determine which number, when multiplied by itself three times, equals 64. 1. **Identify the number**: We can express 64 as \( 4 \times 4 \times 4 \) or \( 4^3 \). 2. **Cube root calculation**: Therefore, the cube root of 64 is: \[ \sqrt[3]{64} = 4 \] ### Part c: \( \sqrt[3]{-27} \) For the cube root of -27, we follow a similar process: 1. **Identify the number**: We can express -27 as \( -3 \times -3 \times -3 \) or \( (-3)^3 \). 2. **Cube root calculation**: Therefore, the cube root of -27 is: \[ \sqrt[3]{-27} = -3 \] ### Summary of Results - \( \sqrt[3]{64} = 4 \) - \( \sqrt[3]{-27} = -3 \)