Find the value of the expression : 1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5

103

Step-by-step explanation:

A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.

1 / (216^ (-2/3)) + 1 / (256^ (-3/4)) + 1 / (243^ (-1/5))

Break it apart into three pieces.

1 / (216^ (-2/3))

216^ (2/3) = 36

1 / (256^ (-3/4))

256^ (3/4) = 64

1 / (243^ (-1/5))

243^ (1/5) = 3

So ...

1 / (216^ (-2/3)) = 36

1 / (256^ (-3/4)) = 64

1 / (243^ (-1/5)) = 3

Add the numbers gives:

36 + 64 + 3 = 103