Question

Which expressions have a value of 64? Check all that apply.

Answer 1

Answer: /..Step-by-step explanation: ..nn

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Answer 2

The correct answer is that none of the expressions listed have a value of 64.

Let's compute the value of each given expression step by step to see which, if any, have a value of 64.

1.
`\(((1)/(4))^3\)`

2.
`\((-(1)/(8))^2\)`

3.
`\(-((1)/(8))^2\)`

4.
`\(((1)/(2))^6\)`

5.
`\(-((1)/(2))^6\)`

We'll start with the first expression and proceed through each one in turn.

Here are the step-wise calculations for each expression:

1.
`\(((1)/(4))^3 = (1)/(4) * (1)/(4) * (1)/(4) = (1)/(64)\), which equals \(0.015625\).`

2.
`\((-(1)/(8))^2 = (-(1)/(8)) * (-(1)/(8)) = (1)/(64)\), which equals \(0.015625\).`

3.
`\(-((1)/(8))^2 = -((1)/(8) * (1)/(8)) = -(1)/(64)\), which equals \(-0.015625\).`

4.
`\(((1)/(2))^6 = (1)/(2) * (1)/(2) * (1)/(2) * (1)/(2) * (1)/(2) * (1)/(2) = (1)/(64)\), which equals \(0.015625\).`

5.
`\(-((1)/(2))^6 = -((1)/(2) * (1)/(2) * (1)/(2) * (1)/(2) * (1)/(2) * (1)/(2)) = -(1)/(64)\), which equals \(-0.015625\).`

None of these expressions have a value of 64. All of them have a value of either
`\(0.015625\)` or
`\(-0.015625\)`, which corresponds to
`\((1)/(64)\)` and
`\(-(1)/(64)\)`, respectively. Therefore, the correct answer is that none of the expressions listed have a value of 64.