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

2 Answers
Oct 28, 2015

Answer:

#(2/3)^(-3) = 27/8 = 3 3/8#

Explanation:

In general #a^(-b) = 1/(A^b)#

So
#color(white)("XXX")(2/3)^(-3) = 1/((2/3)^3)#

#color(white)("XXXXXXXX")= 1/((2^3)/(3^3))#

#color(white)("XXXXXXXX")= (3^3)/(2^3)#

#color(white)("XXXXXXXX")=27/8#

Oct 28, 2015

Answer:

#27/8#

Explanation:

A negative power is the same thing as the positive power of the inverse number.

So, first of all, #(2/3)^{-3}# is the same thing as #(3/2)^3#.

Now we have to compute the power of a fraction, which is very simple, because it is the power of the numerator divided by the power of the denominator, so

#(3/2)^3 = 3^3 / 2^3 = 27/8#