Question

Can someone show me how to simplify (-8x^9/y^-18)^2/3. Please explain step by step. Medal.

Answer 1

\[\huge \left( \frac{ x^n }{ y^n } \right)^m \implies \frac{ x^{n \times m} }{ y^{n \times m} }\]

Answer 2

Try using that and see what you get

Answer 3

First you want tomake everything inside the parenthesis a positive power. Remember, \[\large \frac{1}{x^{-1}} \iff x^1\]

Answer 4

So what can you do with the \(\large y^{-18}\)?

Answer 5

so far I've gotten it down to -8x^6/y^-12

Answer 6

\[\frac{ 1 }{ x^{-n} } \implies x^n \implies \frac{ 1 }{ y^{-18} } \implies y^{18}\]

Answer 7

yeah but it's in a whole set of other things

Answer 8

If you can show your work, we can help guide you

Answer 9

\[\left( -8x^9y^{18} \right)^{2/3}\]

Answer 10

This is what you should have by now, it should be much simpler now.

Answer 11

okay, based on the first thing you showed me I got it from the original to -8x^9*2/3/y^-18*2/3

Answer 12

Trust me, simplify it first.

Answer 13

that's basically the same thing, just split into the two different parts

Answer 14

Because dealing with fractional exponents and negative powers is not pretty.

Answer 15

Naw, making it positive is much better, I didn't see your exponent was negative that's why I gave you that rule first, but this is much simpler to deal with.

Answer 16

\[\large \left(\frac{-8x^9}{\color{red}{y^{-18}}}\right)^{2/3} \implies (-8x^9\color{red}{y^{18}})^{2/3}\]

Answer 17

okay, I understand. so from now on when negative exponents I need to try and make things positive so it isn't so messy?

Answer 18

Yup

Answer 19

Now all you have to do is use the distributive property with your exponent, \(\frac{2}{3}\)

Answer 20

Makes it easier to deal with now just distribute the 2/3

Answer 21

okay let me try really quickly

Answer 22

So instead of going through all trouble writing out the function, :\[\large 9\cdot \frac{2}{3} =~?\]\[\large 18 \cdot \frac{2}{3} = ~?\]

Answer 23

9*2/3=6
18*2/3=12

Answer 24

Good, now just replace your simplified powers into the function.

Answer 25

so now I have -8x^6 y^12

Answer 26

And we missed one small part. We also has to distribute the 2/3 to the -8. \[(-8)^{2/3} = ((-8)^2)^{1/3} = 64^{1/3}= ~?\]

Answer 27

oh okay

Answer 28

it's 4

Answer 29

mmhmm. So your final answer would be?

Answer 30

4x^6 y^12

Answer 31

\[\large \checkmark\]

Answer 32

Thank you for your help! I appreciate it!

Answer 33

No problem :)