College

Which choice is equivalent to the expression below?

[tex]15^0[/tex]

A. 0
B. [tex]15^1[/tex]
C. 15
D. 1

Answer :

To solve the expression [tex]\(15^0\)[/tex], we need to understand the properties of exponents. According to the rules of exponents, any non-zero number raised to the power of 0 is equal to 1. This rule applies to all real numbers except for 0.

Let's break it down step-by-step:

1. Understanding the Rule: The rule for exponents states that any number [tex]\(a\)[/tex] (where [tex]\(a\)[/tex] is not zero) raised to the power of 0 equals 1:
[tex]\[
a^0 = 1 \quad \text{(for any } a \neq 0\text{)}
\][/tex]

2. Applying the Rule: For the given expression [tex]\(15^0\)[/tex], we can apply this rule. Since 15 is a non-zero number, according to the rule, [tex]\(15^0\)[/tex] equals 1.

3. Conclusion: Therefore, the expression [tex]\(15^0\)[/tex] simplifies to 1.

Now, let's match our result with the provided options:

A. 0
B. [tex]\(15^1\)[/tex] (which equals 15)
C. 15
D. 1

The correct choice that matches our result is D. 1.