## anonymous one year ago what is this?? sqrt27u^3v^10w^6

1. anonymous

2. Owlcoffee

$\sqrt{27u^3 v^10 w^6}$ Like this?

3. anonymous

almost. its v to the tenth

4. Owlcoffee

okay, what do you want to with that?

5. anonymous

it says simplify the expression

6. anonymous

and assume all variables are positive

7. Owlcoffee

$\sqrt{27u^3v ^{10}w^6}$ Here you can take advantage of a property of radicals: $\sqrt{u.v}=\sqrt{u}\sqrt{v}$ Si, here, we can take the square root of each factor: $\sqrt{27u^3v ^{10}w^6}=\sqrt{27}\sqrt{u^3}\sqrt{v ^{10}}\sqrt{w^6}$

8. anonymous

oh okay. yeah I remember learning that. but is that the answer?? arent there supposed to to be like, exponents and fractions and stuff?

9. anonymous

dont you do like (27u^3v^10x^6)^1/2

10. Owlcoffee

Yes, but I will not give you the answer, I am not allowed to do that.

11. anonymous

i dont know where to go from there

12. anonymous

i know you cant give the answer. but would you be willing to help me? I dont know where to go after (27u^v^10w^6)^1/2

13. Owlcoffee

If you want to take the method if expressing the main radical as a fractionary exponent, you can take advantage of a exponential property: $(27u^3v ^{10}w^6)^{\frac{ 1 }{ 2 }}$ $(a^n)^m=a ^{mn}$ This expands to each factor, so: $(27^{\frac{ 1 }{ 2 }})(u ^{3\frac{ 1 }{ 2 }})(v ^{10\frac{ 1 }{ 2 }})(w ^{6\frac{ 1 }{ 2 }})$

14. anonymous

and then what? @owlcoffee

15. Owlcoffee

simplify the exponents.

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