Question

s the equation (8–√4)−24×(8–√)16=8−48
true or false?(1 point)
Responses

True
True

False
False
Question 2
Select the response that provides the appropriate justification for the problem above.(1 point)
Responses

Because when the bases are multiplied the exponents are also multiplied.
Because when the bases are multiplied the exponents are also multiplied.

Because the negative exponent rule should be applied.
Because the negative exponent rule should be applied.

Because the equation can be simplified further.
Because the equation can be simplified further.

Because the exponents should be added rather than multiplied.
Because the exponents should be added rather than multiplied.
Question 3
Is the equation (7−4⋅73)49√=7
true or false?

(1 point)
Responses

True
True

False
False
Question 4
Select the response that provides the appropriate justification for the problem above.(1 point)
Responses

Because the answer should be negative because the exponents are negative.
Because the answer should be negative because the exponents are negative.

Because when applying the Quotient Property, the final exponent is NOT 1.
Because when applying the Quotient Property, the final exponent is NOT 1.

Because the Product Property makes the numerator and the denominator equal.
Because the Product Property makes the numerator and the denominator equal.

Because the Quotient Property gives a final exponent of 1.

Answer 1

Let's go through each question step by step.

**Question 1: Is the equation (8–√4)−24×(8–√)16=8−48 true or false?**

To evaluate this expression, first, simplify each part:
- \( \sqrt{4} = 2 \)
- Thus, \( (8 - \sqrt{4}) = (8 - 2) = 6 \).

The left hand side becomes:
- \( 6 - 24 \times (8 - \sqrt{16}) \)
- Since \( \sqrt{16} = 4 \), it becomes \( 6 - 24 \times (8 - 4) = 6 - 24 \times 4 = 6 - 96 = -90 \).

Now, simplify the right hand side:
- \( 8 - 48 = -40 \).

Now, we can compare:
- Left side: -90
- Right side: -40

Since -90 is not equal to -40, the equation is **False**.

**Response for Question 1: False.**

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**Question 2: Select the response that provides the appropriate justification for the problem above.**

Given that we've determined the equation is false, we should choose an explanation that reflects on simplification.

**Response for Question 2: Because the equation can be simplified further.**

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**Question 3: Is the equation (7−4⋅73)49√=7 true or false?**

Let's simplify:
- Start with \( 7 - 4 \cdot 7^3 \).
- Calculate \( 4 \cdot 7^3 \):
\( 7^3 = 343, \) so \( 4 \cdot 343 = 1372 \).
- Therefore, \( 7 - 1372 \) gives \( -1365 \).

Now consider the term \( (49\sqrt{7}) \):
- \( 49\sqrt{7} = 49 \cdot 7^{1/2} = 7^2 \cdot 7^{1/2} = 7^{2.5} = 7^{5/2} \).

Now, equate to 7:
- The left side (after simplification) does not equal 7, which is based on the calculation above.

Thus, the equation is **False**.

**Response for Question 3: False.**

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**Question 4: Select the response that provides the appropriate justification for the problem above.**

From the simplification:
- The left-hand expression resulted in (\( 7^{n} \) form) and the result was not equal to \( 7 \).

Thus, the most appropriate justification points to the end comparison between exponents.

**Response for Question 4: Because the final exponent is NOT 1.**

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Overall responses:
1. False
2. Because the equation can be simplified further.
3. False
4. Because the final exponent is NOT 1.