Is the equation (8–√4)−24⋅(8–√)16=8−48

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

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

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

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

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

Answer 1

To determine whether the equation \( (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48 \) is true or false, let's simplify both sides of the equation.

1. Simplify the left side:

   • \( \sqrt{4} = 2 \) and \( \sqrt{16} = 4 \).
   • Substitute these values into the equation: \[ (8 - 2) - 24 \cdot (8 - 4) \]
   • This simplifies to: \[ 6 - 24 \cdot 4 \]
   • Calculate \( 24 \cdot 4 = 96 \): \[ 6 - 96 = -90 \]

2. Simplify the right side:

   • The right side is: \[ 8 - 48 = -40 \]

3. Compare both sides:

   • Left side: \(-90\)
   • Right side: \(-40\)

Since \(-90 \neq -40\), the equation is false.

The most appropriate justification is: False, because the exponents should be added rather than multiplied.

However, this response does not directly address the simplification error, and the correct approach should recognize the falsehood due to incorrect calculations in the simplification steps rather than exponents specifically.

Thus, if asked, you could answer: False, as the calculations on both sides do not match.