Question

I'm
having trouble figuring this out..

sqrt(3x^7y^-9)*sqrt(6x^8y^13)

Thank you so much!

Answer 1

what do you want to figure out !

Answer 2

use property \(\sqrt{a}\times \sqrt{b}=\sqrt{a\times b}\)

Answer 3

so in this care a is 3x^7y^-9 and b is 6x^8y^13

Answer 4

I need to turn it into the form
\[a \sqrt{b}\]

Answer 5

\[\sqrt{3x^7y^{-9}}\sqrt{6x^8y^{13}}=\sqrt{3x^7y^{-9}6x^8y^{13}}\]

Answer 6

simplify

Answer 7

\[\sqrt{9x^(15)y^4}\]

Answer 8

In other words, sqrt(9x^15v^4)

Answer 9

yes that is good
now reduce it

Answer 10

y^4 and 9 can be reduced to 3y^2
so you get 3y^2sqrt{x^15}

Answer 11

actually where did you get 9
it should be 18 not 9

Answer 12

but you rewrite it like 2x9
so the actual result is 3y^2sqrt{2x^15}

Answer 13

So the final answer was 3x^7y^2sqrt(2x)

And it's correct!

Thanks so much!

Answer 14

yeah you could write that way

Answer 15

what you need to know is that \[a^{p/q}=\sqrt[q]{a^p}\]

Answer 16

it will make your life easier

Answer 17

that is by definition of rational powers

Answer 18

Ok, great! Thank you!