Question

simplify. rewrite the expression in the form $a^n$. $a^5 \cdot a^{-3} =$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponents with the same base \( a \), we use the rule \( a^m \cdot a^n = a^{m + n} \). Here, \( m = 5 \) and \( n=- 3 \).

Step2: Apply the rule

Substitute \( m = 5 \) and \( n=-3 \) into the rule: \( a^{5}\cdot a^{-3}=a^{5+( - 3)} \).

Step3: Simplify the exponent

Calculate \( 5+( - 3)=5 - 3 = 2 \). So the expression simplifies to \( a^{2} \).

Answer:

\(a^{2}\)