How do you evaluate and simplify #27^(2/3)#?

2 Answers
Feb 13, 2017

See the entire solution process below:

Explanation:

First, we can use these rule for exponents to modify this expression:

#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#

#27^(2/3) = 27^(color(red)(1/3) xx color(blue)(2)) = (27^(color(red)(1/3)))^color(blue)(2)#

We can now use rule of roots/exponents to modify the expression within parenthesis:

#x^(1/color(red)(n)) = root(color(red)(n))(x)#

#(27^(1/color(red)(3)))^2 = (root(color(red)(3))(27))^2 = (3)^2 = (3 xx 3) = 9#

Feb 13, 2017

You can also use logarithmic functions, if you have a logarithm table or at least a calculator that can do log functions, if not complex exponential ones.

Explanation:

Using the transformation of #27^(2/3) = (2/3)* log 27#
we calculate
#(2/3) * 1.431 = 0.9542#
Taking the inverse (anti-log, or exponent) of this value gives us the answer:

#10^(0.9542) = 9#