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.

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

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

Answer 1

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

1. Evaluate the left side:

   • \(\sqrt{4} = 2\), so \(8 - \sqrt{4} = 8 - 2 = 6\).
   • Next, \(\sqrt{16} = 4\), so \(8 - \sqrt{16} = 8 - 4 = 4\).
   • Now, calculate \(24 \cdot (8 - \sqrt{16}) = 24 \cdot 4 = 96\).
   • Finally, substituting these values into the left side: \(6 - 96 = -90\).

2. Evaluate the right side:

   • \(8 - 48 = -40\).

3. Compare both sides:

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

Since \(-90\) is not equal to \(-40\), the equation is false.

Therefore, the correct response is:

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