In Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰

Verified step by step guidance

1. Identify the zero-exponent rule, which states that any non-zero number raised to the power of zero is equal to 1.
2. Recognize that the expression \((13y)^0\) involves raising the entire term \(13y\) to the power of zero.
3. Apply the zero-exponent rule to the expression \((13y)^0\).
4. Conclude that the expression simplifies to 1, as any non-zero base raised to the zero power is 1.

Key Concepts

Zero Exponent Rule

The zero exponent rule states that any non-zero base raised to the power of zero equals one. This rule is fundamental in algebra as it simplifies expressions significantly. For example, (13y)⁰ simplifies to 1, regardless of the values of 13 and y, as long as they are not zero.

Exponential Notation

Exponential notation is a way to express repeated multiplication of a number by itself. In the expression (13y)⁰, the base is 13y, and the exponent indicates how many times the base is multiplied. Understanding this notation is crucial for applying the zero exponent rule correctly.

Non-zero Bases

In the context of the zero exponent rule, it is important to note that the base must be non-zero. If the base is zero, the expression 0⁰ is considered indeterminate in mathematics. Therefore, when applying the zero exponent rule, ensuring the base is not zero is essential for valid simplification.