How do you simplify #(64/9)^(3/2)#?

2 Answers
Jan 28, 2018

#(64/9)^(3/2)=sqrt((64/9)^3)#

#=sqrt(262144/729)#

#=512/27#

Jan 28, 2018

#(512)/(27)#

Explanation:

Simplify
#((64)/(9))^((3)/(2))#

This fractional exponent means to find the square root of the numbers raised to the third power.

#sqrt(((64)/(9))^3#

1) Find the square roots of the numbers
#((8)/(3))^3#

2) Raise the numbers to the third power
#(512)/(27)#

#Answer#
#(512)/(27)#

Here's a Khan Academy video about evaluating rational exponents:
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-rational-exp-eval/v/fractional-exponents-with-numerators-other-than-1