Which of the following expressions is equivalent to 216√32713 when applying the exponent properties?(1 point)

Answer 1

To simplify the expression \( 216\sqrt{32713} \) using exponent properties, we first express the square root in terms of exponents.

Recall that the square root of a number can be expressed using a fractional exponent: \[ \sqrt{x} = x^{1/2} \] Thus, we can write: \[ 216\sqrt{32713} = 216 \cdot (32713^{1/2}) \]

Next, if we consider \( 216 \) itself, it can be expressed as \( 216 = 6^3 \). Therefore, we can rewrite the expression entirely in terms of base \( 6 \) and the other term: \[ 216\sqrt{32713} = 6^3 \cdot (32713^{1/2}) \]

So, the expression \( 216\sqrt{32713} \) is equivalent to \( 6^3 \cdot (32713^{1/2}) \).

If you need to combine them further, you could express this in a single term, \[ = 6^3 \cdot 32713^{1/2} \]

However, without additional context or options provided, we can't simplify it further in terms of more elementary expressions or fundamental constants.

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