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

Answer 1

Let's analyze the given equation step by step:

The equation is:

\[ (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48 \]

First, we simplify the components:

1. Calculate \(\sqrt{4}\): \(\sqrt{4} = 2\), so \(8 - \sqrt{4} = 8 - 2 = 6\).

2. Calculate \(\sqrt{16}\): \(\sqrt{16} = 4\), so \(8 - \sqrt{16} = 8 - 4 = 4\).

Now substitute back into the equation:

\[ 6 - 24 \cdot 4 \]

Calculate \(24 \cdot 4\):

\[ 24 \cdot 4 = 96 \]

Now the left side becomes:

\[ 6 - 96 = -90 \]

Now calculate the right side:

\[ 8 - 48 = -40 \]

Now we can compare both sides of the equation:

\(-90 \neq -40\)

Thus, the entire equation is false.

The correct response is:

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

(Note: The response provided is not entirely accurate concerning exponent rules because the equation does not actually involve any exponentiation, but based on the content, it is still false for different reasons.)