AFOQT Practice Test

What happens when you raise an exponent to a power?

1. You multiply the exponents

2. You add the exponents

3. You divide the exponents

4. You subtract the exponents

The correct answer is: You multiply the exponents

When you raise an exponent to a power, you multiply the exponents. This follows the exponentiation rule that states if you have a base raised to a power, and then again raised to another power, you get the base raised to the product of the two exponents. For example, if you start with \( a^{m} \) and raise it to the power of \( n \), you express this mathematically as \( (a^{m})^{n} \). Using the rule, this simplifies to \( a^{m \cdot n} \). Thus, the operation involves multiplying the exponent \( m \) by \( n \) to yield the new exponent. This operation is crucial in simplifying expressions and is a fundamental concept in algebra that applies across various mathematical contexts, from basic arithmetic to more advanced calculus and beyond. Understanding this rule enables one to manipulate complex exponential expressions efficiently.