Need help evaluating this exponent?

Question

(256^1/4 + 64^2/3)²

Answer 1

You can do it on a calculator, or you can think it through:

 

256^1/4 means the fourth root of 256.  The fourth root is the square root of the square root.  The square root of 256 is 16, and the square root of 16 is 4.  So the first term is 4.

 

The 2/3 power is the square of the cube root.  The cube root of 64 is 4 (4 * 4 * 4 = 64), and the square of 4 is 16.  So the second term is 16.

 

Add the terms together to get 20.

 

Now square that, and you get 400.

 

Answer 2

Remember, something like x^1/4 means what is the 4th root of x.  Or rather, what number multiplied by itself 4 times gives you x.  If you have a numerator other than 1, consider rewriting it as follows:

 

• (256^1/4+(64^1/3)²)²     Now we can start working away at this.  Note that 4*4*4*4=256, and 4*4*4=64
• (4+4²)²
• (4+16)²
• 20²
• 400