Question

simplify the expression. assume that the denominator does not equal zero. write any variables in alphabetical order. \\(\frac{12m^{-3}n^6}{2m^{-3}n}\\)

Explanation:

Step1: Simplify coefficients

Divide the coefficient of the numerator (12) by the coefficient of the denominator (2): $\frac{12}{2} = 6$.

Step2: Simplify \( m \)-terms

Use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( m \)-terms: \( \frac{m^{-3}}{m^{-3}} = m^{-3-(-3)} = m^{0}=1 \) (since any non - zero number to the power of 0 is 1).

Step3: Simplify \( n \)-terms

Use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( n \)-terms: \( \frac{n^{6}}{n}=n^{6 - 1}=n^{5} \).

Step4: Combine results

Multiply the simplified coefficient, \( m \)-term result, and \( n \)-term result: \( 6\times1\times n^{5}=6n^{5} \).

Answer:

\( 6n^{5} \)