Question

question 18 (mandatory) (1 point) simplify so that the expression is a single power with a positive exponent: $\left(\frac{k^{4}}{k^{-7}}\
ight)^{-3}$. a) $k^{33}$ b) $\frac{1}{k^{9}}$ c) $\frac{1}{k^{33}}$ d) $k^{9}$

Explanation:

Step1: Simplify inside the parentheses

Use the quotient - rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. Here, $\frac{k^{4}}{k^{-7}}=k^{4-(-7)}=k^{4 + 7}=k^{11}$.

Step2: Apply the power - of - a - power rule

Use the rule $(a^m)^n=a^{mn}$. So, $(k^{11})^{-3}=k^{11\times(-3)}=k^{-33}$.

Step3: Convert to positive exponent

Use the rule $a^{-n}=\frac{1}{a^{n}}$. So, $k^{-33}=\frac{1}{k^{33}}$.

Answer:

C. $\frac{1}{k^{33}}$