How do you simplify #(4x^-1)/(12x^2)#?

Question

Julia Adams · Accepted Answer

#1/3x^-3#

We have the following:

#(color(purple)(4)color(blue)(x^-1))/(color(purple)(12)color(blue)(x^2))#

We can handle these expressions separately. The purple terms just simplify to

#color(purple)(1/3)#

And we can rewrite the blue expressions as follows:

#color(blue)(x^(-1-2))#

We have the same base on the top and bottom, so we can subtract the exponents. Thus, we have

#color(blue)(x^-3)#

Putting it all together, we get

#1/3x^-3#

as our final answer.

Hope this helps!

Abigail Allen · Answer

undefined To simplify (4x^-1)/(12x^2), you can follow these steps:

1. Simplify the numerator: 4x^-1 becomes 4/x.
2. Simplify the denominator: 12x^2 remains the same.
3. Combine the simplified numerator and denominator: (4/x)/(12x^2).
4. To divide by a fraction, multiply by its reciprocal: (4/x) * (1/(12x^2)).
5. Multiply the numerators: 4 * 1 = 4.
6. Multiply the denominators: x * (12x^2) = 12x^3.
7. Simplify the expression: 4/(12x^3).
8. Reduce the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4: 4/4 = 1 and 12x^3/4 = 3x^3.
9. The simplified expression is 1/(3x^3).