multiplying radicals

[MistyRose87]

mutiply and simplify by factoring. Assume that all expressions under radicals represent non-negative numbers.
(^3 square root y^4)(^3 square root 81y^5) all parts of the expression following the square roots are including under the radical.
I am unsure if I am on the right track but thus far I have ^3 square root 81y^9
which would be (^3 square root 9 )(^3 square root y^9)
Can someone please tell me if I am on the right track and if I am not please tell me what I am doing wrong? Thank you in advance.

 

[tkhunny]

Is "^3 square root" actually a "cube root"?

 

[soroban]

Hello, MistyRose87!

\(\displaystyle \text{Mutiply and simplify by factoring: }\;\sqrt[3]{y^4}\cdot\sqrt[3]{81y^5}\)

\(\displaystyle \text{Multiply: }\:\sqrt[3]{y^4}\cdot\sqrt[3]{81y^5} \;=\;\sqrt[3]{81y^9}\)

. . . . . . . . . . . . . . . . .\(\displaystyle =\;\sqrt[3]{27\cdot3 \cdot y^9} \;=\; \sqrt[3]{27}\cdot\sqrt[3]{3}\cdot\sqrt[3]{y^9} \;=\;3\sqrt[3]{3}\,y^3\)

 

[Denis]

(^3 square root y^4)(^3 square root 81y^5)

Next time, show in this style:
CUBEROOT(y^4) * CUBEROOT(81y^5)
or
(y^4)^(1/3) * (81y^5)^(1/3)