Problem 42 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(-\frac{6}{y}\right)^{3}$$

Step-by-Step Solution

Answer

The simplified form of \( \left(-\frac{6}{y}\right)^{3} \) is \( -\frac{216}{y^{3}} \)

Step 1: Apply the exponent to the base

Start by applying the cube (exponent 3) to each part inside the parentheses separately. Remember to include the negative sign. When you apply the cube to a negative number, the result will always be negative, because a negative times a negative is a positive and a positive times a negative is a negative. So \( \left(-6\right)^{3} = -6*-6*-6 = -216 \). Apply the cube to \( y \) and we get \( y^{3} \). The expression then becomes \( -\frac{216}{y^{3}} \)

Step 2: Simplify

Now, you can simplify your expression. Since there are no more operations to apply, your final expression remains \( -\frac{216}{y^{3}} \)