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What is the quotient StartFraction 2 m Superscript 9 Baseline n Superscript 4 Baseline Over Negative 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline EndFractionin simplest form? Assume m not-equals 0, n not-equals 0.
Negative StartFraction m Superscript 12 Baseline n Superscript 6 Baseline Over 2 EndFraction
Negative StartFraction m Superscript 27 Baseline n Superscript 8 Baseline Over 2 EndFraction
6 m Superscript 12 Baseline n Superscript 6 Baseline
8 m Superscript 12 Baseline n Superscript 6 Baseline

Respuesta :

kudzordzifrancis

Answer:

[tex]-\frac{m^{12}n^{6}}{2}[/tex]

Step-by-step explanation:

We want to find the quotient of [tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}[/tex]

We apply the quotient rule of indices to simplify the given exponential expression.

[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

This implies that:

[tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{1}{2}m^{9--3}n^{4--2}[/tex]

We simplify exponents to get:

[tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{1}{2}m^{12}n^{6}[/tex]

Or

[tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{m^{12}n^{6}}{2}[/tex]

Therefore the correct choice is [tex]-\frac{m^{12}n^{6}}{2}[/tex]

onyebuchinnaji

The quotient of the expression after simplification is [tex]- \frac{m^{12} n^{6} }{2}[/tex].

The given parameters:

  • [tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}[/tex]

The quotient of the given expression is obtained by simplifying the expression as follows;

  • [tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}}= - \frac{2}{4} (m^{9 - (-3)} n ^{4 - (-2)}) = - \frac{1}{2} (m^{12}n^{6}) \\\\[/tex]

The quotient of the expression is written as follows;

  • [tex]\frac{2m^9n^4}{-4m^{-3}n^{-2}} = - \frac{m^{12} n^{6} }{2}[/tex]

Thus, the quotient of the expression after simplification is [tex]- \frac{m^{12} n^{6} }{2}[/tex].

Learn more about law of indices here:  https://brainly.com/question/10339517

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