Is the equation (8–√4)−24⋅(8–√)16=8−48 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)

Question

Responses

True, but the equation can be simplified further.
True, but the equation can be simplified further.

False, because the exponents should be added rather than multiplied.
False, because the exponents should be added rather than multiplied.

False, because the Negative Exponent Rule should be applied.
False, because the Negative Exponent Rule should be applied.

True. When the bases are multiplied, the exponents are also multiplied.

Answer 1

Let's evaluate the equation step-by-step.

The equation is \((8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48\).

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

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

2. Substituting those values into the equation: \[ (8 - 2) - 24 \cdot (8 - 4) = 8 - 48 \]

3. Simplify \(8 - 2\) and \(8 - 4\):

   • \(8 - 2 = 6\)
   • \(8 - 4 = 4\)

4. Substituting those simplified values: \[ 6 - 24 \cdot 4 = 8 - 48 \]

5. Calculate \(24 \cdot 4\): \[ 24 \cdot 4 = 96 \]

6. Now substitute back into the equation: \[ 6 - 96 = 8 - 48 \]

7. Simplify the right side \(8 - 48\): \[ 8 - 48 = -40 \]

8. Finish simplifying the left side: \[ 6 - 96 = -90 \]

Now we have: \[ -90 \neq -40 \]

Conclusion:

The equation \((8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48\) is False.

Therefore, the correct justification is: False, because the exponents should be added rather than multiplied.

This option directly corresponds to the evaluation being incorrect rather than an issue with exponent rules, but it is the closest answer among the options provided. The most accurate choice based on the calculation would highlight the values do not equate.