Question

How do you simplify `p^(1/3)timesp^(1/2)`?

Answer 1

See full simplification process below:

Explanation:

The first step is to get each exponent over the same common denominator (in this case `color(red)(6)` by multiplying by a form of `color(blue)(1)` so we can then use the rules for exponents to simplify this expression:

`p^color(red)(1/3) xx p^color(purple)(1/2 ) = p^color(red)(1/3 xx 2/2) xx p^color(purple)(1/2 xx 3/3) = p^color(red)(2/6) xx p^color(purple)(3/6)`

We can now use the following rule for exponents to combine the terms of this expression:

`a^color(red)(a) xx x^color(purple)(b) = x^(color(red)(a)+color(purple)(b))`

Giving

`p^color(red)(2/6) xx p^color(purple)(3/6) = p^(color(red)(2/6)+color(purple)(3/6)) = p^(5/6)`