To determine which number is equivalent to [tex]\(3^4 \div 3^2\)[/tex], follow these steps:
1. Identify the exponents and base:
- The base for both expressions is 3.
- The exponents are 4 and 2.
2. Apply the exponent division rule:
- When you divide numbers with the same base, subtract the exponents:
[tex]\[
a^{b} \div a^{c} = a^{b-c}
\][/tex]
Here, [tex]\(a = 3\)[/tex], [tex]\(b = 4\)[/tex], and [tex]\(c = 2\)[/tex].
3. Subtract the exponents:
- Subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
3^{4-2} = 3^2
\][/tex]
4. Simplify the resulting exponentiation:
- Calculate [tex]\(3^2\)[/tex], which means multiplying 3 by itself:
[tex]\[
3^2 = 3 \times 3 = 9
\][/tex]
Therefore, [tex]\(3^4 \div 3^2\)[/tex] is equivalent to 9.
