Question

question
which expression is equivalent to $3^{-4} \times 3^{6}$

answer
\bigcirc $3^{3}$ \qquad \qquad \bigcirc $\frac{1}{3^{24}}$
\bigcirc $\frac{1}{3^{2}}$ \qquad \qquad \bigcirc $3^{2}$

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m\times a^n=a^{m + n}\). Here, \(a = 3\), \(m=- 4\), and \(n = 6\).

Step2: Apply the rule

Calculate the exponent: \(-4+6 = 2\). So \(3^{-4}\times3^{6}=3^{-4 + 6}=3^{2}\).

Answer:

\(3^{2}\) (the last option)