Well, you know that you can write fractional exponents as radicals...or at least I hope you do...The denominator of the fraction is the index of the radical, and the numerator is a power of x inside the radical.
I'm going to show you how you can do this mentally, without a calculator because when I learned how to solve these, we had to do it mentally.
So this is like saying "the 4th root of x cubed equals 27". (I'm sorry that I have no clue how to type a radical symbol.) Anyway, the first thing I would do is to raise both sides to the 4th power, and no, don't do 27^4...I said I was showing you how to do this mentally. Write it like this...
x^3 = 27 * 27 * 27 * 27
Now you have to take the cube root of both sides, and I hope you know what the cube root of 27 is...(3), so now instead of trying to take the cube root of a large number, you can easily write this as...
x = 3 * 3 * 3 * 3
And you can do that in your head, and if you can't, it's easy math on paper!
(a million/3)^2 - x = 27 -x = 27 - (a million/3)^2 x = (a million/3)^2 - 27 in keeping with risk you meant (a million/3)^(2 - x) = 27. consequently, (a million/3)^(2 - x) = 27 (a million/3)^(2 - x) = (a million/3)^(-3) 2 - x = -3 -x = -5 x = 5
you need to get the x on one side. so you multiply both sides by (4/3). 27 times 4 is 108. then you divide it by three. you get, as your final answer, 36
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Well, you know that you can write fractional exponents as radicals...or at least I hope you do...The denominator of the fraction is the index of the radical, and the numerator is a power of x inside the radical.
I'm going to show you how you can do this mentally, without a calculator because when I learned how to solve these, we had to do it mentally.
So this is like saying "the 4th root of x cubed equals 27". (I'm sorry that I have no clue how to type a radical symbol.) Anyway, the first thing I would do is to raise both sides to the 4th power, and no, don't do 27^4...I said I was showing you how to do this mentally. Write it like this...
x^3 = 27 * 27 * 27 * 27
Now you have to take the cube root of both sides, and I hope you know what the cube root of 27 is...(3), so now instead of trying to take the cube root of a large number, you can easily write this as...
x = 3 * 3 * 3 * 3
And you can do that in your head, and if you can't, it's easy math on paper!
x = 81
Good luck on your exam...Andy...:)
Raise each side to the 4/3 power. Then
x = 27^(4/3) = 3^(3x4/3)= 3^4 = 81
(we convert 27 to 3^3 to get rid of the cube root in the power).
Raise both sides of the equation to the 4th power, then take the cubed root of both sides
[X^(3/4)]^(4/3) = 27^(4/3)
X = 27^(4/3) = 81
(a million/3)^2 - x = 27 -x = 27 - (a million/3)^2 x = (a million/3)^2 - 27 in keeping with risk you meant (a million/3)^(2 - x) = 27. consequently, (a million/3)^(2 - x) = 27 (a million/3)^(2 - x) = (a million/3)^(-3) 2 - x = -3 -x = -5 x = 5
take the cubed root of 27^4..... x will equal 81
you must do this to both sides so the left side will be the cubed root of x^(3/4)^4 and the right side will be the cubed root of 27^4
when you raise x^(3/4) to the fourth, the 4s will cancel out leaving you with x^3, then the cubed root will cancel out the 3s and you are left with x
hope this helps!
It's like saying: "The 4th root of x to the 3rd power = 27"
To solve it, you take the 3rd root and 4th power of each side.
This gives: x=81
if you mean x^(3/4) = 27
then x = 27^(4/3)
that is x = { 27^(1/3) } ^4 = { 3 } ^4 =81
you need to get the x on one side. so you multiply both sides by (4/3). 27 times 4 is 108. then you divide it by three. you get, as your final answer, 36
what is 16x/3/4