How do I simplify this?

[formal coral]

How can I simplify this to the options shown?

[lament drum]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the Moderators, unless someone is breaking the rules. **Do not ping the Helper Moderators, unless there is a conflict between helpers.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[sterile quartz]

bro do (a)^1/3 / (b)^1/3 = (a/b)^1/3

it will solve automatically 😄

i guess answer is D

[formal coral]

How though? Isn’t 32 to the power of 1/3 a decimal?

[outer surge]

use your exponent laws

and yes, it is a decimal, but there is a neat trick

remember simplification in square roots? it is similar

we have $\sqrt[3]{32}=2\sqrt[3]{4}$

[vale fern]

flying green people eater

[formal coral]

How about the exponents for x? If I simplify (13 * 1/3) - (3 * 1/3) won’t I get 10/3?

[outer surge]

yeah

but then you have x^(3+1/3)

BAM

[formal coral]

Where did you get that from? Don’t we multiply the exponents with the exponent of the bracket?

[outer surge]

well

we have x^(10/3), right?

10/3 here is equal to 3+1/3

this is just a mixed number form

so we have $a^{b+c}=a^b\cdot a^c$

[vale fern]

flying green people eater

[outer surge]

one of the exponent laws

[formal coral]

Hmm ok so I end up with x^(3 + 1/3) —> x^3 * x^1/3

How does that help?

[outer surge]

we have a cube and a cuberoot

so we have simplified that term already

now you know what the y term simplifies to, right?

[formal coral]

It just simplifies to y^5 right?

[outer surge]

eh, not really

[formal coral]

OHHH

[outer surge]

yeah

if you're talking about the overall term yes

[formal coral]

I just realized why we made it in terms of a cube and cuberoot lol

[outer surge]

...

yeah, thats good!

[formal coral]

Can you elaborate on the not really part?

[outer surge]

xD

[formal coral]

lol I’m slow

[outer surge]

oh no cause i was thinking that you were talking about the numerator

[formal coral]

Ohh I see

[formal coral]

Alright thank you!!

[outer surge]

yw lol

+close to close post

[iron warren]

@formal coral has given 1 rep to @outer surge

[formal coral]

+close

[thick nexus]

Please thank your Helpers before closing!

Please thank the helpers who assisted you by clicking the buttons below. You can thank each helper only once. Once you're done, click "Close Post" to close this thread.

[thick nexus]

Thank you for your feedback! MATH Weeb 😉 has been awarded 1 . They now have 1 . They have 3 daily left for today.

[thick nexus]

Thank you for your feedback! flying green people eater has been awarded 1 . They now have 16 . They have 2 daily left for today.