Simplify: `root(4)(32x^11y^15)` divided by `root(4)(2x^3y^2)`

2 Answers

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The expression `(root(4)(32x^11*y^15))/(root(4)(2x^3y^2))` has to be simplified.


= `(32x^11*y^15)^(1/4)/(2x^3y^2)^(1/4)`

= `((32x^11*y^15)/(2x^3y^2))^(1/4)`

= `(32/2)^(1/4)*x^((11-3)/4)*y^((15 - 2)/4)`

= `16^(1/4)*x^(8/4)*y^(13/4)`

= `2*x^2*y^(13/4)`

The simplified form of `(root(4)(32x^11*y^15))/(root(4)(2x^3y^2)) = 2*x^2*y^(13/4)`

Zaca's profile pic

Zaca | Student, Undergraduate | (Level 1) Salutatorian

Posted on

Since both the numerator and the denominator are to the fourth root, another way to write the equation is:


We can simplify inside the root by dividing like terms:


Then take the fourth root (if possible!) of each part under the root (16, x, and y):

`root(4)16 = 2`

`root(4)(x^8) = x^2`

`root(4)(y^13) = y^3(root(4)y)`

Put them together can you get:


` `