Question

Which expression is equivalent to StartFraction (2 m n) Superscript 4 Baseline Over 6 m Superscript negative 3 Baseline n Superscript negative 2 Baseline EndFraction? Assume m not-equals 0, n not-equals 0. StartFraction 8 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction StartFraction 10 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction StartFraction 8 m Superscript 16 Baseline n Superscript 12 Baseline Over 3 EndFraction StartFraction m Superscript 4 Baseline n Superscript 6 Baseline Over 3 EndFraction

Answer 1

Answer: A or first one

Answer 2

`(8m^7n^6)/(3)`

Explanation:

`((2mn)^4)/(6m^(-3)n^(-2))=(2^4)/(6)m^(4-(-3))n^(4-(-2))=\boxed{(8m^7n^6)/(3)}`

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The applicable rules of exponents are ...

(a^b)^c = a^(bc)

1/a^b = a^-b

(a^b)(a^c) = a^(b+c)