Question

Simplify the expression.

fraction with negative 5 times the quantity 3 minus the cube root of 27 times 2 end quantity as the numerator and 3 as the denominator

six fifths
5
negative six fifths
−5

Answer 1

Let's simplify the expression step-by-step.

We start with the expression:

\[
\frac{-5(3 - \sqrt[3]{27} \cdot 2)}{3}
\]

First, we can compute the cube root of \(27\):

\[
\sqrt[3]{27} = 3
\]

Now substitute this value back into the expression:

\[
\frac{-5(3 - 3 \cdot 2)}{3}
\]

Next, simplify \(3 \cdot 2\):

\[
3 \cdot 2 = 6
\]

Now substitute that into the expression:

\[
\frac{-5(3 - 6)}{3}
\]

This simplifies to:

\[
\frac{-5(-3)}{3}
\]

Now, simplify \(-5(-3)\):

\[
-5 \cdot -3 = 15
\]

We are left with:

\[
\frac{15}{3}
\]

Finally, divide:

\[
\frac{15}{3} = 5
\]

Thus, the simplified expression is:

\[
\boxed{5}
\]