How do you write the simplified form of -64^(1/ 3)?

2 Answers
Apr 24, 2018

the simplified answer would be -4

Explanation:

Let's factor out 64:
64=2^6
-(2^6)^(1/3)
=-2^(6.(1/3))
=-2^2
=-4

Apr 24, 2018

-4

Explanation:

Recall one of the laws of indices:

sqrtx = x^(1/2)" "and " "root3(x) = x^(1/3)

-64^(1/3) = root3(-64)

64 is a perfect cube: 64=4^3

root3(-64) =-4

You could also work with the prime factors:

root3(-64) = root3(-(2^6))

=-2^2

=-4

Note that perfect cubes can be negative, but perfect squares cannot.