what is the quotient of $\frac{2^{4}}{2^{-4}}$?\n$\frac{1}{256}$\n$\frac{1}{2}$\n$1$\n$256$
what is the quotient of $\frac{2^{4}}{2^{-4}}$?\n$\frac{1}{256}$\n$\frac{1}{2}$\n$1$\n$256$
Answer
Explanation:
Step1: Use exponent - division rule
According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{2^{4}}{2^{-4}}$, we have $a = 2$, $m = 4$, $n=-4$. Then $2^{4-(-4)}$.
Step2: Simplify the exponent
$4-(-4)=4 + 4=8$. So we get $2^{8}$.
Step3: Calculate $2^{8}$
$2^{8}=2\times2\times2\times2\times2\times2\times2\times2 = 256$.
Answer:
D. 256