QuestionAugust 26, 2025

Which expressions are equivalent to (m^-18)/(m^-12) Choose all that apply. A. m^30 B. ((1)/(m))^-6 C. ((1)/(m))^6 D. m^-6 E. m^6 F. m^-30

Which expressions are equivalent to (m^-18)/(m^-12) Choose all that apply. A. m^30 B. ((1)/(m))^-6 C. ((1)/(m))^6 D. m^-6 E. m^6 F. m^-30
Which expressions are equivalent to (m^-18)/(m^-12) Choose all that apply. A. m^30 B. ((1)/(m))^-6 C. ((1)/(m))^6 D. m^-6 E. m^6 F. m^-30

Solution
4.3(200 votes)

Answer

C. (\frac {1}{m})^{6} ### D. m^{-6} Explanation 1. Simplify the expression Use the property of exponents \frac{a^m}{a^n} = a^{m-n} to simplify \frac{m^{-18}}{m^{-12}} to m^{-18 - (-12)} = m^{-6}. 2. Evaluate each option A. m^{30} is not equivalent to m^{-6}. B. (\frac{1}{m})^{-6} = m^{6}, which is not equivalent to m^{-6}. C. (\frac{1}{m})^{6} = m^{-6}, which is equivalent to m^{-6}. D. m^{-6} is equivalent to m^{-6}. E. m^{6} is not equivalent to m^{-6}. F. m^{-30} is not equivalent to m^{-6}.

Explanation

1. Simplify the expression<br /> Use the property of exponents $\frac{a^m}{a^n} = a^{m-n}$ to simplify $\frac{m^{-18}}{m^{-12}}$ to $m^{-18 - (-12)} = m^{-6}$.<br />2. Evaluate each option<br /> A. $m^{30}$ is not equivalent to $m^{-6}$.<br /> B. $(\frac{1}{m})^{-6} = m^{6}$, which is not equivalent to $m^{-6}$.<br /> C. $(\frac{1}{m})^{6} = m^{-6}$, which is equivalent to $m^{-6}$.<br /> D. $m^{-6}$ is equivalent to $m^{-6}$.<br /> E. $m^{6}$ is not equivalent to $m^{-6}$.<br /> F. $m^{-30}$ is not equivalent to $m^{-6}$.
Click to rate:

Similar Questions