Simplify each exponential expression in Exercises 23–64. $x^0{y}^5$

Verified step by step guidance

1. Recall the zero exponent rule: for any nonzero base \(a\), \(a^0 = 1\). This means \(x^0 = 1\) as long as \(x \neq 0\).
2. Apply the zero exponent rule to \(x^0\), so \(x^0\) simplifies to 1.
3. Rewrite the original expression \(x^0 y^5\) by substituting \(x^0\) with 1, giving \(1 \cdot y^5\).
4. Since multiplying by 1 does not change the value, the expression simplifies to just \(y^5\).
5. Therefore, the simplified form of the expression \(x^0 y^5\) is \(y^5\).

Key Concepts

Zero Exponent Rule

Any nonzero base raised to the zero power equals 1. For example, x^0 = 1, regardless of the value of x (as long as x ≠ 0). This rule simplifies expressions by eliminating variables raised to the zero power.

Product of Powers

When multiplying variables with exponents, if the bases are the same, you add the exponents. Although not directly needed here, understanding this helps in simplifying expressions with multiple exponential terms.

Simplifying Exponential Expressions

Simplifying involves applying exponent rules to rewrite expressions in simpler forms. For x^0 y^5, applying the zero exponent rule and keeping y^5 as is results in the simplified form y^5.