The question "What is the exponent of 8?" is incomplete. It is asking about the exponent but doesn't specify what the base is or what we are trying to express. A better phrasing of the question would be:
- "If we are raising a number to the eighth power, what is the exponent?"
- "What does the exponent '8' represent when raising a number to the eighth power?"
Here's a breakdown addressing this, incorporating the provided reference:
Understanding Exponents
An exponent indicates how many times a base number is multiplied by itself. In the context of the question, the reference states that the eighth power of a number 'n' is calculated by multiplying 'n' by itself eight times, expressed as:
n8 = n × n × n × n × n × n × n × n
This directly implies that the number '8' here is the exponent. It signifies the number of times we are multiplying the base number, 'n', by itself.
Key Points
- Base: In the expression n8, 'n' is the base number. It's the number being multiplied.
- Exponent: The number '8' is the exponent, indicating how many times the base is multiplied by itself. It is always written as a superscript to the right of the base number.
Examples
| Expression | Base | Exponent | Meaning | Result |
|---|---|---|---|---|
| 28 | 2 | 8 | 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 | 256 |
| 58 | 5 | 8 | 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 | 390625 |
| 108 | 10 | 8 | 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 | 100000000 |
Summary
- When we talk about the "eighth power," the exponent is always 8.
- The exponent '8' means the base number is used as a factor eight times.
Therefore, when referring to the eighth power, the exponent is specifically 8.
