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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponentiation
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. The exponent indicates how many times the base is multiplied by itself. For example, in the expression 3^5, 3 is the base and 5 is the exponent, meaning 3 is multiplied by itself five times: 3 × 3 × 3 × 3 × 3.
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the expression -3^5, the exponentiation is performed before applying the negative sign.
When dealing with negative numbers and exponents, it is crucial to understand how the negative sign interacts with the exponent. In the expression -3^5, the negative sign is not included in the exponentiation, meaning it evaluates as -(3^5). This results in a negative outcome, as the base (3) is raised to the power of 5 first, and then the negative sign is applied.