Question

1. what is equivalent to $4^2 \cdot 4^4$?

$4^8$
$16^6$
$4^6$
$16^8$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$. For $4^2 \cdot 4^4$, base $a=4$, $m=2$, $n=4$.
$4^2 \cdot 4^4 = 4^{2+4}$

Step2: Calculate the sum of exponents

Add the exponents 2 and 4.
$4^{2+4} = 4^6$

Answer:

$\boldsymbol{4^6}$ (Option C)