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# Evaluating fractional exponents

Sal shows how to evaluate 64^(2/3) and (8/27)^(-2/3). Created by Sal Khan.

## Want to join the conversation?

• At , can you explain why the reciprocal eliminates the negative sign? What does flipping the fraction do that makes it a positive?
• 2^0 is 2/2 is just 1. This is because 2^1=2 and dropping 1 power divides by 2, 2/2=1. (This trick works for every exponet value, dropping 1 more gives 2^0-1, gives 1/2.)
• So is x^2/3 the same thing as finding the cube root of x, and then squaring it? (or vice versa)
• . He is correct. (27)^2/3=the cube root of 27 and square it=3^2=9
• I'm stuck on a problem.
How would you simplify the following: (x^3)^(2/3)

My first thought would be to multiply the exponents: 3/1 * 2/3 which would leave me with an exponent of 2. Can anyone confirm this answer for me?
• If my brain does not fail me I think that's correct. The answer is x^2.
• at did Sal mean numerator
• how do you make this solution work when you are working with negatives? Example: (-7776)^(2/5) or 〖4096〗^(-5/6)
• With a negative number inside the root, you cannot take the root if it is even (the denominator of the fraction), but it if it is odd, then the answer will end up negative. 7776 = 6^5 (rather than going through factoring, I did 7776^(1/5) in calculator), so squaring we end up with (-6)^2 which ends up as 36. With a negative exponent, this causes the expression to reciprocate and change exponent to positive, so start with 1/(4096)^(5/6) = 1/4^5 = 1/1024.
• well what if something was like 1/2 to the power of 7 how would you
solve that?
• (1/2)^7 is telling you to multiply: 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2
Hope this helps.
• I have a question..
Why is (-9)^1/2 not a real number?
• What number can you multiply by itself to get a negative number? A positive times a positive is positive, but also a negative times a negative is positive.
• What do do when a fraction is squared by a fraction?
• If a fraction is raised to the power of a fraction, for eg.
if 2/7 is raised to the power of 7/9, then 2/7 would be under the root of 9, and 2/7 would be raised to the power of 7 when it's under.
HOPE THIS HELPS,
THANK YOU