Question

Evaluate the following:

`3^-2 xx 2^0 - (27)^(-1/3)`

Answer 1

Given expression: `3^-2 xx 2^0 - (27)^(-1/3)`

Step-wise calculation:

1. Simplify each term using the laws of indices:

`3^-2 = 1/3^2`

`3^-2 = 1/9`

2⁰ = 1   ...(Since any nonzero number to the power 0 is 1)

`(27)^(-1/3) = (3^3)^(-1/3)`

`(27)^(-1/3) = 3^(3 xx -1/3)`

`(27)^(-1/3) = 3^-1`

`(27)^(-1/3) = 1/3`

2. Substitute back into the expression:

`1/9 xx 1 - 1/3 = 1/9 - 1/3`

3. Find a common denominator and subtract:

The common denominator for 9 and 3 is 9, so write `1/3` as `3/9`.

`1/9 - 3/9 = (1 - 3)/9`

`1/9 - 3/9 = (-2)/9`