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Usimov [2.4K]
3 years ago
8

Mc105-1.jpg

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0
The right answer is HL.
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Which expression is equivalent to ( 4mn / m^-2n^6)^-2
inn [45]

Here are a few rules with exponents that apply here:

  1. Raising a power to a power: (x^m)^n=x^{m*n}
  2. Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
  3. Converting negative exponents to positive ones: x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m

Firstly, solve the outer exponent:

(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}

Next, divide:

\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}

Next, convert the negative exponents:

4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}

<u>Your final answer is n^10/16m^6 , or B.</u>

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(a + b - c )(a + b + c )
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