Question

Consider the expression (-3)^-3 divided by 1/-6^2What three choices are equivalent to the expression given

Answer 1

We can interpret the question as follows:

`((-3)^(-3))/((1)/(-6^2))`

Then, we have that:

`((-3)^(-3))/((1)/(-6^2))=((1)/((-3)\cdot(-3)\cdot(-3)))/(-(1)/(6^2))=((1)/(-27))/(-(1)/(6^2))=(-(1)/(27))/(-(1)/(6^2))=((1)/(27))/((1)/(6^2))=(6^2)/(27)=(36)/(27)`

For the answer above, we use the next exponents' rules:

`a^(-1)=(1)/(a),a^(-n)=(1)/(a^n)`

We can simplify the fraction as follows:

1. The factors for 36 are 2²* 3².

2. The factors for 27 are 3³.

Then, we have:

`(2^2\cdot3^2)/(3^3)=(2^2\cdot3^2)/(3^2\cdot3)=(3^2)/(3^2)\cdot(2^2)/(3)=1\cdot(4)/(3)=(4)/(3)`

Then, the simplified expression for the fraction is equal to 4/3.