How do you Simplify 4^(7/3) - 12^(4/3)? Please Step by Step

[mgmarygg]

Homework Statement

(Square Root Exponents) 4^(7/3) - 12^(4/3)

For this problem The answer is 4x^2 - 12x but i tried i could not seem to obtain the same answer, could you please explain on how to do this step by step so I know do the rest of other problems

Homework Equations

The Attempt at a Solution

stuck :( 3√4x)⁷ - (3√12x)⁴
= (3√4⁷x⁷) - (3√12⁴x⁴)...

 

[Mark44]

Homework Statement

(Square Root Exponents) 4^(7/3) - 12^(4/3)

For this problem The answer is 4x^2 - 12x but i tried i could not seem to obtain the same answer, could you please explain on how to do this step by step so I know do the rest of other problems

What exactly is the problem? From the title it looks like you need to simplify 4^7/3 - 12^4/3, but this has absolutely nothing to do with 4x² - 12x.

And what do "square root exponents" mean?

Homework Equations

The Attempt at a Solution

stuck :( 3√4x)⁷ - (3√12x)⁴
= (3√4⁷x⁷) - (3√12⁴x⁴)...

 

[jedishrfu]

I think the correct equation is:

4 x ^ (7/3) - 12 x ^ (4/3)

Remember that x ^ (7/3) = x^2 * x ^ (1/3)

and that x ^ (4/3) = x * x^(1/3)

 

[e^(i Pi)+1=0]

Assuming the above expression is correct, don't forget that you can factor out exponents. Don't let the fact that they're fractions distract you.