Final answer:
The power to a power rule is used when raising an exponent to another exponent (e.g., (5^3)^4 = 5^12), and it involves multiplying the exponents. The multiplying powers rule applies when multiplying numbers with the same base (e.g., 5^3 * 5^2 = 5^5), which involves adding exponents.
Step-by-step explanation:
Understanding Exponent Rules: Power to a Power vs. Multiplying Powers
The power to a power rule and the multiplying powers rule are two different operations used in mathematics when dealing with exponents.
Power to a Power Rule
This rule applies when you raise an exponent to another exponent. An example is (53)4. To apply the power to a power rule, you multiply the exponents together: 3 * 4 = 12, resulting in 512.
Multiplying Powers Rule
When two numbers with the same base are multiplied together, you add their exponents. For example, 53 * 52 is simplified by adding the exponents: 3 + 2, resulting in 55.
In conclusion, the power to a power rule involves multiplying exponents when an exponentiated number is raised to another exponent, while multiplying powers with the same base involves adding exponents.