Question

3^{-6} \times left(3^{4} div 3^{0}
ight)^{2}

Explanation:

Step1: Simplify the exponent in the parentheses

Using the rule of exponents \(a^m\div a^n = a^{m - n}\), for \(3^4\div3^0\), we have \(m = 4\), \(n = 0\), so \(3^4\div3^0=3^{4 - 0}=3^4\).

Step2: Square the result from Step 1

Now we have \((3^4)^2\). Using the rule \((a^m)^n=a^{m\times n}\), we get \(3^{4\times2}=3^8\).

Step3: Multiply with the other term

We now have \(3^{- 6}\times3^8\). Using the rule \(a^m\times a^n=a^{m + n}\), we add the exponents: \(-6 + 8 = 2\), so \(3^{-6}\times3^8 = 3^{2}\).

Answer:

\(3^{2}\)