Is the equation 612⋅(6–√)3=36

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

False, because the exponents should be divided.
False, because the exponents should be divided.

False, because the exponents should be multiplied.
False, because the exponents should be multiplied.

True, according to the Product Property.
True, according to the Product Property.

True, according to the Power of a Power Property.

Answer 1

To evaluate the equation \( 612 \cdot (6 - \sqrt{3}) = 36 \), we first simplify the left side of the equation.

1. Evaluate \( 612 \cdot (6 - \sqrt{3}) \):

   • The term \( 612 \) is likely a typo or misunderstanding, and it's unclear what it represents without further context.
   • However, if we assume it meant \( 6^{12} \), this is a large number and will significantly exceed 36.

2. Compare with the right side (36):

   • \( 6^{12} \) is way larger than 36, indicating that whatever the left side resolves to, it will not be equal to 36.

3. Assessing the responses:

   • The responses focus on exponent rules, but since the left-hand side is substantially larger, the equation does not hold true.
   • Therefore, the answer is: False, because the exponents should be divided. is the most relevant, but it over-explains the reason.

In conclusion, the simplest answer is False, as the left side far exceeds 36, and the initial interpretations concerning laws of exponents do not apply to this concrete evaluation where the fundamental calculations show the left side is far greater.