Question

simplify. assume that no variable equals 0.\\(
\frac{12m^{8}y^{6}}{-9my^{4}}\\)
\\(\circ -\frac{4m^{7}y^{2}}{3}\\)
\\(\circ -\frac{4m^{7}y^{-2}}{3}\\)
\\(\circ -\frac{4m^{7}}{3y^{2}}\\)
\\(\circ \frac{4m^{7}y^{2}}{3}\\)

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{12}{-9} \). We can divide both numerator and denominator by their greatest common divisor, which is 3. So \( \frac{12\div3}{-9\div3} = -\frac{4}{3} \).

Step2: Simplify \( m \) terms

Using the quotient rule for exponents \( \frac{a^m}{a^n}=a^{m - n} \), for the \( m \) terms \( \frac{m^8}{m} = m^{8 - 1}=m^7 \).

Step3: Simplify \( y \) terms

Again, using the quotient rule for exponents, for the \( y \) terms \( \frac{y^6}{y^4}=y^{6 - 4}=y^2 \).

Step4: Combine all simplified parts

Multiply the simplified coefficient, \( m \) term, and \( y \) term together. We get \( -\frac{4}{3}\times m^7\times y^2=-\frac{4m^7y^2}{3} \).

Answer:

\( -\frac{4m^7y^2}{3} \) (which corresponds to the first option: \( -\frac{4m^7y^2}{3} \))