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:

$\frac{(-3)^{-3}}{\frac{1}{-6^2}}$

Then, we have that:

$\frac{(-3)^{-3}}{\frac{1}{-6^2}}=\frac{\frac{1}{(-3)\cdot(-3)\cdot(-3)}}{-\frac{1}{6^2}}=\frac{\frac{1}{-27}}{-\frac{1}{6^2}}=\frac{-\frac{1}{27}}{-\frac{1}{6^2}}=\frac{\frac{1}{27}}{\frac{1}{6^2}}=\frac{6^2}{27}=\frac{36}{27}$

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

$a^{-1}=\frac{1}{a},a^{-n}=\frac{1}{a^n}$

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:

$\frac{2^2\cdot3^2}{3^3}=\frac{2^2\cdot3^2}{3^2\cdot3}=\frac{3^2}{3^2}\cdot\frac{2^2}{3}=1\cdot\frac{4}{3}=\frac{4}{3}$

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