Math problem help?

Question

Simplify:
cubed root of 135x^4y^13

Answer 1

Hi,

First factor 135 into its prime factors. You are looking for 3 of the same factor so you can take something out of the radical. 135 factors into 3 x 3 x 3 x 5, so because there are three 3s, you can put a 3 in front of the radical. The 5 stays inside.

Then look at each exponent and divide it by 3. The number of times that 3 divides into the exponent is the power on that letter in front of the radical. If there is a remainder, that tells the exponent on the variable inside the radical sign.

On x, 3 goes into 4 once with a remainder of one. That means that x^1 or x is out front and there is also an x remaining inside.

On y, 3 goes into 13 four times with a remainder of one. That means that x^4 is out front and there is also an x remaining inside.

Your final answer is:

...............___
...........3/
3xy^4.\/...5xy

I hope that helps!! :-)

Answer 2

cubed root of 135x^4y^13
= {27*5 x^3*x y^12*y}^1/3
= 3xy^4(5xy)^1/3

Answer 3

135x^4 y^13
=(3*3*3*5)(x^3*x)(y^12*y)
Therefore
(135 x^4 y^13)^1/3
=(3^3*5)^1/3 (x^3*x)^1/3(y^12*y)^1/3
=(3*5^1/3)(x*x^1/3)(y^4*y^1/3)
=3xy^4 cube-root(5xy)

Answer 4

135 = 5 * 27

27 = 3^3

3xy4 *cube root 5xy

Answer 5

3cubed root5x^52y