Question

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

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

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \times a^n = a^{m+n}$.
$3^{-4} \times 3^{6} = 3^{-4+6}$

Step2: Calculate the exponent

Simplify the sum in the exponent.
$3^{-4+6} = 3^{2}$

Answer:

$3^2$ (the option D. $3^2$)