Question

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

Answer 1

103

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