Question

Priya says, "I can figure out 5⁰ by looking at other powers of 5. 5³ is 125, 5² is 25, then 5¹ is 5." What concept is Priya explaining, and how is she using it to understand 5⁰?

Answer 1

Priya is exploring the concept of integer powers and how reducing the exponent by one results in dividing the number by itself. By observing the pattern in powers of five, she deduces that, in general, any non-zero number to the power of zero equals 1.

Step-by-step explanation:

Priya is using the concepts of integer powers and mathematical patterns to understand what 5⁰ equals. In mathematics, when we raise a number to a power, we are multiplying that number by itself a certain number of times. Priya is observing a pattern in the powers of five:

• 5³ = 125
• 5² = 25
• 5¹ = 5

As the exponents decrease by 1, the result is the previous result divided by 5. Extending this pattern to 5⁰, which has an exponent 1 less than 5¹, would mean dividing 5 by 5, resulting in the answer of 1. This illustrates the general principle that any non-zero number raised to the power of zero is equal to 1.