Which of the following expressions represents a⁰ x aⁿ?

Which of the following expressions represents a⁰ x aⁿ?

• A. aⁿ
• B. a⁰⁺ⁿ
• C. a⁰⁻ⁿ
• D. a⁰ⁿ

Answer: (B)

When considering the expression \(a^0 \times a^n\), it's important to apply the properties of exponents. The key rule to remember is that when multiplying two expressions with the same base, you add their exponents. In this case, the base is \(a\) and you have the exponents \(0\) (from \(a^0\)) and \(n\) (from \(a^n\)). By using the property of exponents: \[ a^0 \times a^n = a^{0 + n} \] This simplifies to: \[ a^{n} \] This means that \(a^0 \times a^n\) can also be expressed as \(a^{0 + n}\). Hence, the correct representation of the product of these two expressions is indeed \(a^{0+n}\). So, the correct answer captures the addition of the exponents, showcasing the fundamental rule of combining similar bases in exponential expressions.

When considering the expression (a^0 \times a^n), it's important to apply the properties of exponents. The key rule to remember is that when multiplying two expressions with the same base, you add their exponents.

In this case, the base is (a) and you have the exponents (0) (from (a^0)) and (n) (from (a^n)). By using the property of exponents:

[

a^0 \times a^n = a^{0 + n}

]

This simplifies to:

[

a^{n}

]

This means that (a^0 \times a^n) can also be expressed as (a^{0 + n}). Hence, the correct representation of the product of these two expressions is indeed (a^{0+n}).

So, the correct answer captures the addition of the exponents, showcasing the fundamental rule of combining similar bases in exponential expressions.