Final answer:
The question is about the base case in computepowers() function for handling exponentiation where the exponent is zero. The base case should return 1 since any non-zero number raised to the power of zero is 1, reflecting the multiplicative identity property. This illustrates a fundamental rule of exponents in mathematics.
Step-by-step explanation:
The concept is regarding exponents in mathematics. Specifically, it is concerning what happens when the exponent value is zero. According to the rules of exponents, any non-zero number raised to the power of zero is 1. This is because of the idea that an exponent indicates how many instances of a number are multiplied together. If we have zero instances, the implicit 1 is all that remains, which is the base case for multiplication - just like zero is for addition. Hence, the base case for the function compute powers() should return 1 when the val variable is equal to 0, illustrating the concept that any number to the power of zero is 1.
As an example, we look at how exponents are multiplied together. For instance, (5³)* is equivalent to (5 × 5 × 5)4, which means multiplying 5 by itself 12 times, giving us 5¹². Similarly, reducing an expression like 2³ to 2· 10¹² to 3 × 10⁵ shows that there can be many ways to reach the same answer in mathematics. Another aspect to consider, beyond integer exponents, is when dealing with non-integer values such as 3¹.⁷, which is mathematically defined and calculable with tools like a calculator.