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Is 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 the exponents should be added rather than multiplied.
Because the exponents should be added rather than multiplied.

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

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

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 Quotient Property gives a final exponent of 1.
Because the Quotient Property gives a final exponent of 1.

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

1 answer

Let's evaluate each equation one by one and provide the necessary justifications.

Question 1:

Is the equation \((8 - \sqrt{4}) - 24 \times (8 - \sqrt{16}) = 8 - 48\) true or false?

  1. Calculate \( \sqrt{4} \) and \( \sqrt{16} \):

    • \( \sqrt{4} = 2 \)
    • \( \sqrt{16} = 4 \)

  2. Substitute these values: \[ (8 - 2) - 24 \times (8 - 4) = 8 - 48 \] \[ 6 - 24 \times 4 = 8 - 48 \] \[ 6 - 96 = -40 \] And on the right side: \[ 8 - 48 = -40 \]

So, the equation \( (8 - \sqrt{4}) - 24 \times (8 - \sqrt{16}) = 8 - 48 \) is True.

Question 2:

Select the response that provides the appropriate justification for the problem above.

The correct justification for the first question is:

  • Because the equation can be simplified further.

Question 3:

Is the equation \( (7^{-4} \cdot 7^3)^{49} = 7 \) true or false?

  1. Combine the exponents using the Product Property: \[ 7^{-4 + 3} = 7^{-1} \]

  2. Now raise this to \( 49 \): \[ (7^{-1})^{49} = 7^{-49} \]

Thus, \( 7^{-49} \) does not equal \( 7 \). Therefore, the equation \( (7^{-4} \cdot 7^3)^{49} = 7 \) is False.

Question 4:

Select the response that provides the appropriate justification for the problem above.

The correct justification for the third question is:

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

Summary:

  1. True
  2. Because the equation can be simplified further.
  3. False
  4. Because when applying the Quotient Property, the final exponent is NOT 1.