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Keith_Richards [23]
3 years ago
13

Which expression is equivalent to [4mn/m⁻2n⁻6}⁻2? Assume m and n do not equal zero

Mathematics
2 answers:
leva [86]3 years ago
8 0
The answer would be {(n^5)^2}/{(4*m^3)^2} = { n^{10} }/{16*m^6}
Ilia_Sergeevich [38]3 years ago
6 0

Answer:

Given Expression is

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

To find the equivalent expression we need the following results.

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

2. x^a\times x^b=x^{a+b}

3.  \frac{x^a}{x^b}=x^{a-b}

4. (x^a)^b=x^{ab}

Consider,

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

=(\frac{m^{-2}n^{-6}}{4mn})^{2}

=\frac{1^2}{4^2}\times(\frac{m^{-2}n^{-6}}{mn})^{2}

=\frac{1}{16}\times(m^{-2-1}\times n^{-6-1})^2

=\frac{1}{16}\times(m^{-3}\times n^{-7})^2

=\frac{1}{16}\times(\frac{1}{m^{3}n^{7}})^2

=\frac{1}{16}\times\frac{1^2}{(m^{3}n^{7})^2}

=\frac{1}{16}\times\frac{1}{m^{3\times2}n^{7\times2}}

=\frac{1}{16}\times\frac{1}{m^6n^{14}}

=\frac{1}{16m^6n^{14}}

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