Which of the following expressions is equivalent to 216√32713

Question

when applying the exponent properties?(1 point)
Responses

2
2

8
8

12
Start Fraction 1 over 2 End Fraction

18

Answer 1

To simplify the expression \(216\sqrt{32713}\) and find an equivalent expression using exponent properties, let's first break it down.

1. Recognize that \(216\) can be expressed as \(6^3\) (since \( 6 \times 6 \times 6 = 216\)).
2. The square root can be expressed as an exponent: \(\sqrt{32713} = 32713^{1/2}\).

So we could rewrite the original expression as:

\[ 6^3 \cdot 32713^{1/2} \]

Next, we assess if we can simplify this expression further or relate it to any of the choices provided.

However, the choices given (2, 8, 12, \( \frac{1}{2} \), 18) do not directly correlate with the expression we have.

Since \(6^3\) is quite distinct and does not directly simplify to any provided choices, there seems to be no suitable simplification linking back to any of the given responses based on exponent properties.

If further clarification is possible, could you provide additional context? Based on the given options, none relate directly to what we derived mathematically.