Which of the following expressions is equivalent to 216√32713 when applying the exponent properties?(1 point)
Responses
8
8
12
Start Fraction 1 over 2 End Fraction
2
2
18
18
The correct expression that is equivalent to 216√32713 when applying the exponent properties is:
(32713)^(1/3)
To find the expression that is equivalent to 216√32713 using exponent properties, we need to simplify the expression by applying the properties.
The expression 216√32713 can be written as:
(216)^(1/2) * (32713)^(1/2)
Now, let's simplify each term separately:
(216)^(1/2) simplifies to √216, which can be further simplified as follows:
√216 = √(2^3 * 6^2)
Using the property √(a * b) = √a * √b, we can simplify it as:
√(2^3) * √(6^2) = 2^(3/2) * 6^(2/2) = 2^(3/2) * 6^1 = 2^(3/2) * 6
Next, let's simplify (32713)^(1/2) as √32713.
Putting it all together, the expression equivalent to 216√32713 when applying the exponent properties is:
2^(3/2) * 6 * √32713