simplify rational equations=? how to you do this............... 6x to the 4th power/18x to the second power

Question

PLEASE HELP>

Answer 1

6x^4/18x^2 Take 6/18=1/3 and then take 4-2=2
So 6x^4/18x^2 =x^2/3

Answer 2

It should be x^2 / 3

Using law of indices,
a^m / a^n = a^(m-n)

Hence x^4 / x^2 = x^(4-2) = x^2
Divide 18 by 6 and you get x^2/3

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Alternatively use substitution method

Let x^2 be y

Hence 6x^4 / 18x^2 = 6x^[2(2)] / 18x^2 = 6y^2/18y = y/3
Sub y back as x^2, and you get x^2/3

(x^4 can be expressed as x^[2(2)] because of another law of indices:
a^x = a^mn, if x=mn)

Answer 3

The first answer is correct. If you want to think about it simplistically, think about what an exponent is - repeated multiplication. So let's write it is 6 x x x x / 18 x x. You can cancel " x x " from both numerator and demoninator (equivalent to dividing the numerator and demonator by x^2) and you get 6 x x / 18 = x x / 3 = (x^2)/3

Answer 4

What point of math are you taking? by ability of graphing, you may tell, it has the minimum, yet there are actually not any optimal. It is going to beneficial infinity. by ability of recognizing x being raised to the 2d potential and co-effecient being beneficial (ONE), you realize the graph opens UP. meaning there is minimum, yet no optimal. to try this mathmatically, you will ought to contain calculus, and artwork with derivatives like this: y=x^2-6x+7 y'=2x-6 ... locate the 1st by-made of the function locate the element the place slope turns into 0 0=2x-6; x=3 for the reason that there is in uncomplicated terms one element the place y' is 0, there is in uncomplicated terms one element the place curve transformations guidelines y''=2 ... 2d derivative for the reason that 2d derivative is beneficial, that's concave UP meaning graph comes from beneficial infinity down wards and while x=3, it transformations direction and is going as much as the infinity. you may take any of the above solutions reckoning on your grade. complication-loose algebra to calculus....

Answer 5

1/3^2

I think - Good Luck

Answer 6

6x^4
--------- = x^2/3
18x^2