College

Which choice is equivalent to the expression below?

[tex]30^0[/tex]

A. 1
B. 30
C. 0
D. [tex]30^2[/tex]

Answer :

To solve the expression [tex]\(30^0\)[/tex], we can use an important rule of exponents: Any non-zero number raised to the power of 0 is equal to 1. This rule applies universally in mathematics.

Here's a simple breakdown to understand why:

1. The rule can be understood through the pattern of reducing exponents. For example:
- [tex]\(30^3 = 30 \times 30 \times 30\)[/tex]
- [tex]\(30^2 = 30 \times 30 = \frac{30^3}{30}\)[/tex]
- [tex]\(30^1 = 30 = \frac{30^2}{30}\)[/tex]
- Continuing the pattern, [tex]\(30^0 = \frac{30^1}{30} = 1\)[/tex]

2. It's essential to remember that this rule applies to any non-zero base number, regardless of what that number is.

Thus, the expression [tex]\(30^0\)[/tex] simplifies to 1.

So, the equivalent choice for the expression is:

A. 1