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

A

Step-by-step explanation:EDGE (not sure if im right let me know)

Answer 2

Question

Which expression is equivalent to
`(4mn)/(m^(-2)n^6)`. Assuming
`m \\eq 0; n\\eq 0`

Answer:

`(4m^3)/(n^5)`

Explanation:

Given

`(4mn)/(m^(-2)n^6)`

Required:

Simplify

To simplify this, we start by splitting each individual function

`(4mn)/(m^(-2)n^6) = (4m)/(m^(-2)) * (n)/(n^6)`

From laws of indices

`(a^x)/(a^y) = a^(x-y)`

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

`(4m)/(m^(-2)) * (n)/(n^6) = 4m^(1-(-2)) * n^(1-6)`

`(4m)/(m^(-2)) * (n)/(n^6) = 4m^(1+2)) * n^(1-6)`

`(4m)/(m^(-2)) * (n)/(n^6) = 4m^(3) * n^(-5)`

From laws of indices,

`a^(-x) = (1)/(a^x)`

So,

`(4m)/(m^(-2)) * (n)/(n^6) = 4m^(3) * (1)/(n^5)`

`(4m)/(m^(-2)) * (n)/(n^6) = (4m^3)/(n^5)`

Hence,
`(4mn)/(m^(-2)n^6)` is equivalent to
`(4m^3)/(n^5)`