SOLUTION: Hey all! Can someone help me out with my studyplan? I want to get this! How do I write 64^-2/3= in radical notation? And then evaluate the expression? Thanks in advance!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hey all! Can someone help me out with my studyplan? I want to get this! How do I write 64^-2/3= in radical notation? And then evaluate the expression? Thanks in advance!       Log On


   

Question 767752: Hey all!
Can someone help me out with my studyplan? I want to get this!
How do I write 64^-2/3= in radical notation?
And then evaluate the expression?
Thanks in advance!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%282%2C1%2C%22%22%2C64%5E%28-2%2F3%29%29 
It helps if you know things like 4³=64 and ∛64 = 4 

Positive fractions can be written as radicals, but
negative exponents can't, so we have to put 1 over
them with a positive exponent.  Then we use the 
"fraction exponential to radical" rule, which is

matrix%282%2C1%2C%22%22%2C+A%5E%28B%2FC%29%29%22%22=%22%22%28root%28C%2CA%29%29%5EB


matrix%282%2C1%2C%22%22%2C64%5E%28-2%2F3%29%29%22%22=%22%22matrix%282%2C1%2C%22%22%2C1%2F64%5E%222%2F3%22%29%22%22=%22%22

Now we use the "fraction exponent to radical" rule

matrix%282%2C1%2C%22%22%2C1%2F%28root%283%2C64%29%29%5E2%29%22%22=%22%22

and since we know that ∛64 = 4

that becomes

1%2F%284%5E2%29 

and finally

1%2F16

Edwin