Is the equation 3−5⋅(81√4)33−4=3−6 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point) Responses True. All rules have been applied correctly. True. All rules have been applied correctly. False. There is an error in applying the Product Property. False. There is an error in applying the Product Property. True, but the equation should be simplified using the Negative Exponent Rule. True, but the equation should be simplified using the Negative Exponent Rule. False. There is an error in calculation using the Quotient Property.

Answer 1

To determine whether the equation \( 3 - 5 \cdot (81 \sqrt{4})^{33 - 4} = 3 - 6 \) is true or false, we will simplify and calculate each side of the equation.

First, let's simplify the left side:

1. Calculate \( 33 - 4 = 29 \), so we need to evaluate \( (81 \sqrt{4})^{29} \).
2. We know \( \sqrt{4} = 2 \), thus \( 81 \sqrt{4} = 81 \cdot 2 = 162 \).
3. Therefore, \( (81 \sqrt{4})^{29} = (162)^{29} \).
4. Now multiply by -5: \( -5 \cdot (162)^{29} \).

Now examining the right side:

1. \( 3 - 6 = -3 \).

Now we rewrite the original expression:

• Left Side: \( 3 - 5 \cdot (162)^{29} \)
• Right Side: \( -3 \)

Now we can conclude:

1. \( 3 - 5 \cdot (162)^{29} \) will be a very large negative number because \( (162)^{29} \) is a very large positive number, and multiplying it by -5 gives a large negative result when added to 3.
2. The left side is much less than -3.

Since \( 3 - 5 \cdot (162)^{29} \) is not equal to -3, we find that the equation is false.

Therefore, the correct response is: False. There is an error in applying the Product Property.