Question

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

False. There is an error in applying the Product Property.
False. There is an error in applying the Product Property.

False. There is an error in calculation using the Quotient Property.
False. There is an error in calculation using the Quotient Property.

True. All rules have been applied correctly.
True. All rules have been applied correctly.

True, but the equation should be simplified using the Negative Exponent Rule.

Answer 1

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

1. **Left Side**:
- First, simplify \( \sqrt{4} \):
\[ \sqrt{4} = 2 \]
- Now replace \( \sqrt{4} \) in the equation:
- \( (81 \sqrt{4})^{33} = (81 \cdot 2)^{33} = (162)^{33} \)
- Therefore, we rewrite the left side:
\[ 3 - 5 \cdot (162)^{33} - 4 \]

2. **Combine Constants**:
- \( 3 - 4 = -1 \)
- So now we have:
\[ -1 - 5 \cdot (162)^{33} \]

3. **Now compare this to the right side**:
- The right side:
\[ 3 - 6 = -3 \]

Now we have simplified both sides:
- Left Side: \( -1 - 5 \cdot (162)^{33} \)
- Right Side: \( -3 \)

Now, to conclude:
- Since \( -1 - 5 \cdot (162)^{33} \) (a very large negative number) is not equal to \( -3 \), the equation is **false**.

Thus, the correct answer is:

**False. There is an error in applying the Product Property.**

However, the reason is primarily due to differences in scalar arithmetic rather than Product Property specifically. The nature of the simplification reflected an error in interpreting the equation rather than the Product Property, so a more general understanding of calculation could be appropriate as well.