Multiply and Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. ?

Question

³√y10 ³√81y11 = ____ ??

Simplify and Type in radical form.

Thanks tons!

Answer 1

Best Answer - Chosen by Voters

Hi, first of all we must write the expression as a single root. Remembering that a root is just a power with exponent a<1, we can write
³√y10 ³√81y11 =
= ((y^10)^(1/3))(81y^11)^(1/3) =
= (y^10 * 81y^11)^(1/3) =
= (81y^21)^(1/3) =
= 81^(1/3) * (y^21)^(1/3) =
= (3^4)^(1/3) * y^(21/3) =
= 3^(4/3) * y^7 = 3*3^(1/3) * y^7 = 3(³√3)y^7.
Of course I assumed that 10 and 11 before y were exponents.
I hope I helped. Bye!