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2 months ago

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Which expression is equivalent to (StartFraction 4 m n Over m Superscript negative 2 Baseline n Superscript 6 Baseline EndFracti

on) Superscript negative 2? Assume m not-equals 0, n not-equals 0. StartFraction n Superscript 6 Baseline Over 16 m Superscript 8 Baseline EndFraction StartFraction n Superscript 10 Baseline Over 16 m Superscript 6 Baseline EndFraction StartFraction n Superscript 10 Baseline Over 8 m Superscript 8 Baseline EndFraction StartFraction 4 m cubed Over n Superscript 8 Baseline EndFraction

2 answers:

PIT_PIT [12.4K]2 months ago

5 0

Question

Which expression is equivalent to $\frac{4mn}{m^{-2}n^6}$ . Assuming $m \neq 0; n\neq 0$

Answer:

$\frac{4m^3}{n^5}$

Step-by-step explanation:

Given

$\frac{4mn}{m^{-2}n^6}$

Required:

Simplify

To achieve simplification, we begin by dividing each function individually

$\frac{4mn}{m^{-2}n^6} = \frac{4m}{m^{-2}} * \frac{n}{n^6}$

According to the properties of indices

$\frac{a^x}{a^y} = a^{x-y}$

Thus, the aforementioned expression can be restated similarly

$\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1-(-2)} * n^{1-6}$

$\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{1+2)} * n^{1-6}$

$\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * n^{-5}$

From the indices laws

$a^{-x} = \frac{1}{a^x}$

So,

$\frac{4m}{m^{-2}} * \frac{n}{n^6} = 4m^{3} * \frac{1}{n^5}$

$\frac{4m}{m^{-2}} * \frac{n}{n^6} = \frac{4m^3}{n^5}$

Therefore, $\frac{4mn}{m^{-2}n^6}$ can be regarded as $\frac{4m^3}{n^5}$

Inessa [12.5K]2 months ago

5 0

Answer:

Option D on Edg

Step-by-step explanation:

Just completed the test

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