Question

How do you rewrite this expression in simplest radical form: `(4x^3y^4)^(3/2)`?

Answer 1

The simplified version is `8y^6x^4 sqrt(x)`

Explanation:

When you take an exponent of an exponent, it's equal to multiplying both exponents together. Using this tip, we can distribute the `3/2` exponent as follows:

NOTE: When I color something `color(red)("red")` it means it's in the simplest form.

`(4x^3y^4)^(3/2)=4^(3/2)xx x^(3*3/2)xx y^(4*3/2)`

`=4^(3/2)xx x^(9/2)xx y^(12/2)`

`=4^(3/2)xx x^(9/2)xx color(red)(y^6)`

Next, lets simplify the first two terms:

`4^(3/2)=(4^(1/2))^3=(sqrt(4))^3 = 2^3=color(red)(8)`

`x^(9/2)=x^(4 1/2)=color(red)(x^4 sqrt(x))`

Finally, let's reassemble:

`(4x^3y^4)^(3/2)=color(red)(8y^6 x^4 sqrt(x))`