How do you simplify #\frac { x ^ { - 1 } } { 4 x ^ { 4 } }#?

Answer 1

Avery Alexander

#1/(4x^5)#

Our expression can be rewritten as

#1/4 (x^(-1)/x^4)#

At this point, the variables are all that need to be considered.

We will then make use of the exponent property.

#(x^a)/(x^b)=x^(a-b)#

This simply states that exponents are subtracted when the bases are the same. Using this, we obtain

#1/4 (x^(-1-4))#

which further reduces to

#1/4 x^-5#

If you're not comfortable with the negative exponent, we can easily bring it to the denominator. This will get us closer to

#1/4 x^-5=1/(4x^5)#

I hope this is useful.

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Answer 2

Isaiah Anthony

To simplify ( \frac{x^{-1}}{4x^4} ), you can first rewrite ( x^{-1} ) as ( \frac{1}{x} ). Then, you can combine the terms in the numerator and the denominator using the properties of exponents. This yields ( \frac{1}{4x^5} ).

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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.