Question

simplify.
rewrite the expression in the form $4^n$.
\\(\dfrac{4^{11}}{4^{-8}} = \square\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $\frac{a^m}{a^n} = a^{m - n}$. Here, the base $a = 4$, $m = 11$, and $n = -8$.

Step2: Apply the rule

Substitute the values into the formula: $4^{11 - (-8)}$. Simplify the exponent: $11 - (-8) = 11 + 8 = 19$. So the expression simplifies to $4^{19}$.

Answer:

$4^{19}$