Question

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

Answer 1

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

How to determine the equivalent expression?

The expression is given as:

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

Apply the law of indices

$(4m^{1 + 2}n^{1-6})^{-2$

Evaluate the sum and the differences

$(4m^{3}n^{-5})^{-2$

Apply the negative exponent

$\frac{1}{16m^{2*3}}}n^{5*2}$

Evaluate

$\frac{1}{16m^{6}}n^{10}$

Rewrite as:

$\frac{n^{10}}{16m^{6}}$

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

Read more about equivalent expressions at:

brainly.com/question/2972832

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