Question

3^4 · 3^2 =
○ 3^6
○ 6^6
○ 9^3
○ 3^8

Explanation:

Step1: Recall exponent rule

When dividing exponents with the same base, we use the rule \(a^m\div a^n=a^{m - n}\). Here, the base \(a = 3\), \(m = 4\), and \(n = 2\).

Step2: Apply the rule

For \(3^4\div3^2\), using the rule \(a^m\div a^n=a^{m - n}\), we substitute \(a = 3\), \(m = 4\), \(n = 2\). So we get \(3^{4-2}=3^2\)? Wait, no, wait. Wait, the problem is \(3^4-3^2\)? Wait, no, the original problem is \(3^4 - 3^2\)? Wait, no, looking at the image, it's \(3^4-3^2=\)? Wait, no, maybe it's a typo, maybe it's \(3^4\div3^2\)? Because the options are all exponents. Wait, let's check the options. Let's re - examine. If it's \(3^4\div3^2\), then using \(a^m\div a^n=a^{m - n}\), \(3^{4 - 2}=3^2\)? No, the options are \(3^6\), \(6^6\), \(9^3\), \(3^8\). Wait, maybe the problem is \(3^4\times3^2\)? Because \(3^4\times3^2=3^{4 + 2}=3^6\), which is one of the options (the first option is \(3^6\)). Let's assume it's a multiplication (maybe a typo in the problem, division would give \(3^2 = 9\), not in the options, multiplication gives \(3^6\)). So if we assume the problem is \(3^4\times3^2\), then:
Using the exponent rule \(a^m\times a^n=a^{m + n}\), where \(a = 3\), \(m = 4\), \(n = 2\). Then \(3^4\times3^2=3^{4 + 2}=3^6\).

Answer:

\(3^6\) (the first option: \(3^6\))