what is the quotient of $\frac{7^{-1}}{7^{-2}}$?\n$\frac{1}{343}$\n$\frac{1}{7}$\n$7$\n$49$
what is the quotient of $\frac{7^{-1}}{7^{-2}}$?\n$\frac{1}{343}$\n$\frac{1}{7}$\n$7$\n$49$
Answer
Explanation:
Step1: Use exponent - division rule
According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{7^{-1}}{7^{-2}}$, we have $m=-1$ and $n = - 2$. So, $\frac{7^{-1}}{7^{-2}}=7^{-1-(-2)}$.
Step2: Simplify the exponent
Calculate $-1-(-2)=-1 + 2=1$. So, $7^{-1-(-2)}=7^{1}$.
Step3: Evaluate the result
Since $7^{1}=7$.
Answer:
7