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Which expression is equivalent to (4mn/m^-2n^6)^-2

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MrRoyal

The expression that is equivalent to (4mn/m^-2n^6)^-2 is [tex]\frac{n^{10}}{16m^{6}}[/tex]

How to determine the equivalent expression?

The expression is given as:

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

Apply the law of indices

[tex](4m^{1 + 2}n^{1-6})^{-2[/tex]

Evaluate the sum and the differences

[tex](4m^{3}n^{-5})^{-2[/tex]

Apply the negative exponent

[tex]\frac{1}{16m^{2*3}}}n^{5*2}[/tex]

Evaluate

[tex]\frac{1}{16m^{6}}n^{10}[/tex]

Rewrite as:

[tex]\frac{n^{10}}{16m^{6}}[/tex]

Hence, the expression that is equivalent to (4mn/m^-2n^6)^-2 is [tex]\frac{n^{10}}{16m^{6}}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/2972832

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