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

Question

True, but the equation can be simplified further.

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

False, because the Negative Exponent Rule should be applied.

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

Answer 1

Let's simplify the left side of the equation step by step to see whether it is equal to the right side.

The equation is: \[ (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) \]

Start with simplifying the square roots: \[ \sqrt{4} = 2 \quad \text{and} \quad \sqrt{16} = 4 \] So, substituting these back into the equation, we have: \[ (8 - 2) - 24 \cdot (8 - 4) \]

Now simplify inside the parentheses: \[ 6 - 24 \cdot 4 \]

Next, calculate \(24 \cdot 4\): \[ 24 \cdot 4 = 96 \]

Now, substitute that back into the equation: \[ 6 - 96 \]

Finally, calculate \(6 - 96\): \[ 6 - 96 = -90 \]

Now, look at the right side of the equation: \[ 8 - 48 = -40 \]

So, we see that: \[ -90 \neq -40 \]

Thus, the equation is false. The correct response is: False, because the exponents should be added rather than multiplied.