This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here are the solutions for each part:
*a) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 8. Step 3: Calculate the cube root. The number in the placeholder is .
*b) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 1. Step 3: Calculate the cube root. The number in the placeholder is .
*c) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 64. Step 3: Calculate the cube root. The number in the placeholder is .
*d) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 27. Step 3: Calculate the cube root. The number in the placeholder is .
*e) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 125. Step 3: Calculate the cube root. The number in the placeholder is .
*f) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number such that . This can be written as . Step 2: To find , we take the cube root of 216. Step 3: Calculate the cube root. The number in the placeholder is .
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*a) Calculate the value of the number in the placeholder: Step 1: The problem is to find a number x such that x × x × x = 8.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.