Question

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. (\frac{3^6}{3^3} = square)
(type exponential notation with positive exponents.)
b. the expression cannot be simplified.

Explanation:

Step1: Recall exponent rule

When dividing exponents with the same base, use the rule \( \frac{a^m}{a^n} = a^{m - n} \) (where \( a
eq 0 \), \( m \) and \( n \) are real numbers). Here, \( a = 3 \), \( m = 6 \), \( n = 3 \).

Step2: Apply the rule

Substitute into the rule: \( \frac{3^6}{3^3} = 3^{6 - 3} \).

Step3: Simplify the exponent

Calculate \( 6 - 3 = 3 \), so \( 3^{6 - 3} = 3^3 \).

Answer:

\( 3^3 \) (and the correct choice is A)