Question

Evaluate the expression. Write fractions in simplest form. $$ \left(\frac{6}{2}\right)^{3} $$

Short answer

The expression \((\frac{6}{2})^{3}\) simplifies to 27.

Step-by-step solution

Perform Division

First, execute the division inside the parentheses. \( \frac{6}{2} = 3 \). So, the revised expression is \(3^{3}\).

Apply Exponentiation

Now compute the expression \(3^{3}\). This is achieved by multiplying 3 by itself twice, as the exponent tells us how many times to multiply the base (3) by itself. Hence, \(3^{3} = 3 * 3 * 3 = 27\).

Simplify Result

The result, 27, cannot be further simplified as the exercise didn’t result in a fraction. Hence, the expression \((\frac{6}{2})^{3}\) evaluates to 27.