Final answer:
In mathematics, you multiply the exponents when you have a power of a power exponent problem. This is part of the laws of exponents and helps simplify expressions like (5³)⁴ into 5¹² by multiplying the exponents 3 and 4 to get 12.
Step-by-step explanation:
The student's question refers to a specific scenario in exponentiation in mathematics. You only ever multiply the exponents for a power of a power exponent problem. This rule is a part of the laws of exponents, which deals with how to handle powers when performing operations such as multiplication, division, or raising powers to another power.
For example, when you have an expression like (5³)⁴, this is equivalent to saying you have four groups of 5³ multiplied together. To simplify, you would multiply the exponents: 3 * 4 = 12. Thus, (5³)⁴ = 5¹².
- When multiplying two numbers with the same base, add the exponents (e.g., 10³ * 10² = 10⁵).
- When raising a power to another power (a power of a power), multiply the exponents (e.g., (2³)² = 2⁶).
- If you have zero as the exponent, the result is 1 because zero instances of the number will leave the implicit 1 (e.g., 5⁰ = 1).