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How do you simplify #(4xy)^-2#?

Answer 1

#1/(16x^2y^2)#

The negative index means that the whole bracket can be written in the denominator first to get rid of the minus. (Find the reciprocal)

#(4xy)^-2 = 1/(4xy)^2#

Now square everything in the bracket.

#1/(4xy)^2 = 1/(16x^2y^2)#

The alternative was to square each factor in the numerator, but the indices will all be negative, and have to be moved to the denominator separately.

The first method is probably quicker and easier.

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Answer 2

Nathan Axel

To simplify (4xy)^-2, you can use the property of negative exponents, which states that a^-n = 1/(a^n). Applying this property, (4xy)^-2 becomes 1/(4xy)^2. Expanding (4xy)^2 results in 16x^2y^2. So, (4xy)^-2 simplifies to 1/(16x^2y^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.