Question

What simplifies into 2mn^2×^3√5mn^2

Answer 1

We have: 2mn^2 √5mn^2, where √ is a cubed root.

Hence, we can do (2mn^2)^3 to get 8m^3n^6. Now we'll take that into the root:

√5mn^2*8m^3n^6 = √120m^4n^8

So, √120m^4n^8 simplifies into 2mn^2 √5mn^2.

Answer 2

`2\sqrt[3]{5}m^(2)n^(4)`

Explanation:

`2mn^2*\sqrt[3]{5}mn^2`

Let us bring the term of same type together we get

`2*\sqrt[3]{5}* mn^2 * mn^2`

`2\sqrt[3]{5}* mn^2* mn^2`

`2\sqrt[3]{5}* m* m* n^2* n^2`

Now here we apply the rule of exponents , which is like this

m^p\times m^q=m^{p+q}

Hence

`2\sqrt[3]{5}* m^(1+1)* n^(2+2)`

`2\sqrt[3]{5}* m^(2)* n^(4)`

`2\sqrt[3]{5}m^(2)n^(4)`

Hence this is our answer.