Question

Simplify the expression completely. (assume all variables are positive)

sqrt (9a^12 b^-10)

Answer 1

Basically, if an exponent is negative, flip it upside down. For example:
\[x ^{-10}=\frac{ 1 }{ x ^{10} }\]
\[\frac{ 3 }{ x ^{-5} }=3x ^{5} \]Basically you can do that with your negative exponent. You just move it to the bottom to make it positive.

Answer 2

I tried this as an answer 3a sqrt 1/b^10 and still did not accept that answer. Am I doing something wrong

Answer 3

I apologize, I didn't see that you wrote sqrt x_x

Answer 4

\[\sqrt{9a ^{12}b ^{-10}}\]correct?

Answer 5

\[3a \sqrt{b^-10}\] is the answer I got but wont accept it I assume because the whole (assume all vairiables are positive). Yes the forumula you pu is correct

Answer 6

Alright, awesome. Well the first thing to know is what I wrote above, about how you can move negative exponents around. So I can start by rewriting the problem like this:
\[\sqrt{\frac{ 9a ^{12} }{ b ^{10} }}\]Kinda understand this part?

Answer 7

yes, this way there are no negative exponents

Answer 8

Alright, cool. Now this is just to make sure, but do we know:
\[\sqrt{x ^{2}}\] and what that is? It may sound lke a stupid question, but I just want to be sure.

Answer 9

\[x ^{1/2}\]?

Answer 10

It would just be x.
\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }}\], but since we have that x^2 under the root, it just reduces to x.

Answer 11

ok makes sense

Answer 12

Alright. So the next bit of important info is this:
\[\sqrt{x ^{2}}=\sqrt{x}*\sqrt{x}\]If you know how to factor, we can actually do this. Another example:
\[\sqrt{18}=\sqrt{2}*\sqrt{3}*\sqrt{3}\]
That make sense?

Answer 13

yes

Answer 14

Okay, cool. So if we can factor something inside of the square root, we can break it apart like this. So let's do that with your problem. I'llstart with the top and rewrite it:
\[\sqrt{9a ^{12}}=\sqrt{9}*\sqrt{a ^{2}}*\sqrt{a ^{2}}*\sqrt{a ^{2}}*\sqrt{a ^{2}}*\sqrt{a ^{2}}*\sqrt{a ^{2}}\]You see why?

Answer 15

yes 9 is sqrt alone then we just break down the exponent of a^12

Answer 16

Correct. So all 7 of those square roots can simply. We get 9 to become 3 and those other 6 all become a. So that means it'll simplify to:
\[3a ^{6} \]

Answer 17

and bottom would break down to \[\sqrt{b10}*\sqrt{b10}*\sqrt{b10}*\sqrt{b10}*\sqrt{b10}\]

Answer 18

This can also be done with the b on the bottom.
\[\sqrt{b ^{10}}=\sqrt{b ^{2}}*\sqrt{b ^{2}}*\sqrt{b ^{2}}*\sqrt{b ^{2}}*\sqrt{b ^{2}} \]

Answer 19

ment 2 right lol copy past messed up so \[\sqrt{b^5}\]

Answer 20

Well, b^5, but no root. Each of those 5 b^2 roots just become b, so you have b^5 on bottom to finally get:
\[\frac{ 3a ^{6} }{ b ^{5} }\]

Answer 21

If you notice, when the power under a square root is even, you can just divide it by 2 and that will be how many you have outside of the root. So even something like:
\[\sqrt{x ^{1204}}=x ^{602}\]can easily be done, just divide by 2 when you see the power is even.

Answer 22

Oh ok I got it yeah not flipping it inside the sqrt is the main thing I was doing, thank you so much

Answer 23

yeah, np :3