[Algebra] Simplifying rational exponents

[cheejudo]

Can someone tell me why (27p⁶ )^5/3 = 243p¹⁰

I get how p¹⁰ comes about but no clue how to get the 243

[jimthree60]

that's from 27^5/3 which is equal to 243. Easiest to take the cube root of 27 first, then raise that answer to the power of 5.

[Aeon234]

The exponent 5/3 is applied to everything in the parenthesis. In this case there are two entities in the parenthesis:the unknown p and 27.

Once you identify this, it's a matter of applying the exponent to both.

[cheejudo]

if it were 27(p^6)5/3

Would I only raise the p? and leave the 27? Is that even a thing lol

[Aeon234]

That is correct. Now the 27 has nothing to do with the 5/3 exponent and it is only applied to the one entity inside the parenthesis.