Question

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

Answer 1

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 simplify this, we start by splitting each individual function

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

From laws of indices

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

SO, the above expression can also be expressed the same way

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

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

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

From laws of indices,

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

So,

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

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

Hence, $\frac{4mn}{m^{-2}n^6}$ is equivalent to $\frac{4m^3}{n^5}$

Answer 2

Answer:

Option D on Edg

Step-by-step explanation:

Just did the test