Which expression is equivalent to (4^0)-^3•4-^2

Answer 1

To simplify the expression \((4^0) - 3 \cdot 4^{-2}\), we can follow these steps:

1. Calculate \(4^0\): \[ 4^0 = 1 \]

2. Calculate \(4^{-2}\): \[ 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \]

3. Substitute these values into the expression: \[ 1 - 3 \cdot \frac{1}{16} \]

4. Multiply \(3\) by \(\frac{1}{16}\): \[ 3 \cdot \frac{1}{16} = \frac{3}{16} \]

5. Now, substitute this value back into the expression: \[ 1 - \frac{3}{16} \]

6. To subtract \(\frac{3}{16}\) from \(1\), convert \(1\) to a fraction with a denominator of 16: \[ 1 = \frac{16}{16} \]

7. Now perform the subtraction: \[ \frac{16}{16} - \frac{3}{16} = \frac{16 - 3}{16} = \frac{13}{16} \]

Thus, the equivalent expression is: \[ \boxed{\frac{13}{16}} \]

Answer 2

Which expression is equivalent to (2 -^1/2^0)-^2

Answer 3

To simplify the expression \((2^{-1/2}) - 2^0\), we will evaluate each component step-by-step.

1. Calculate \(2^0\): \[ 2^0 = 1 \]

2. Calculate \(2^{-1/2}\): \[ 2^{-1/2} = \frac{1}{2^{1/2}} = \frac{1}{\sqrt{2}} \]

3. Now substitute these values back into the expression: \[ \left(\frac{1}{\sqrt{2}}\right) - 1 \]

4. To perform this subtraction, we can convert \(1\) to a fraction with a denominator of \(\sqrt{2}\): \[ 1 = \frac{\sqrt{2}}{\sqrt{2}} \]

5. Substitute this back into the expression: \[ \frac{1}{\sqrt{2}} - \frac{\sqrt{2}}{\sqrt{2}} = \frac{1 - \sqrt{2}}{\sqrt{2}} \]

Thus, the equivalent expression is: \[ \frac{1 - \sqrt{2}}{\sqrt{2}} \]

If you also want to rationalize the denominator, you can multiply the numerator and denominator by \(\sqrt{2}\): \[ \frac{(1 - \sqrt{2})\sqrt{2}}{2} = \frac{\sqrt{2} - 2}{2} \]

Either form is valid, depending on whether or not you'd like to rationalize the denominator. Thus, we can express the final answers as:

1. \(\frac{1 - \sqrt{2}}{\sqrt{2}}\)
2. Or, when rationalized: \(\frac{\sqrt{2} - 2}{2}\)

Choose the format that suits your needs!

Answer 4

Which expression is equivalent to (2-^1 / 2^0)

Answer 5

To simplify the expression \(2^{-1} / 2^0\), we'll look at each component separately:

1. Calculate \(2^0\): \[ 2^0 = 1 \]

2. Calculate \(2^{-1}\): \[ 2^{-1} = \frac{1}{2} \]

3. Now substitute these values into the expression: \[ \frac{2^{-1}}{2^0} = \frac{\frac{1}{2}}{1} = \frac{1}{2} \]

Thus, the expression \(2^{-1} / 2^0\) simplifies to: \[ \frac{1}{2} \]

Therefore, the final answer is: \[ \boxed{\frac{1}{2}} \]

Answer 6

2 -^1 not 2 -^ (-1)

Answer 7

Thank you for the clarification.

To evaluate the expression \(2^{-1} / 2^0\), we will simplify it step by step.

1. Calculate \(2^0\): \[ 2^0 = 1 \]

2. Calculate \(2^{-1}\): \[ 2^{-1} = \frac{1}{2} \]

3. Now substitute these values into the expression: \[ 2^{-1} / 2^0 = \frac{1/2}{1} = \frac{1}{2} \]

Thus, the expression \(2^{-1} / 2^0\) simplifies to: \[ \frac{1}{2} \]

If you meant \(2 - (2^{-1})\), please let me know, and I can help evaluate that expression instead. Otherwise, the final answer remains: \[ \boxed{\frac{1}{2}} \]

Answer 8

Which expression is equivalent to (6^0) -^2/6-^2

Answer 9

To simplify the expression \((6^0) - 2 \cdot 6^{-2}\), we can follow these steps:

1. Calculate \(6^0\): \[ 6^0 = 1 \]

2. Calculate \(6^{-2}\): \[ 6^{-2} = \frac{1}{6^2} = \frac{1}{36} \]

3. Substitute these values back into the expression: \[ 1 - 2 \cdot \frac{1}{36} \]

4. Multiply \(2\) by \(\frac{1}{36}\): \[ 2 \cdot \frac{1}{36} = \frac{2}{36} = \frac{1}{18} \]

5. Now substitute this value into the expression: \[ 1 - \frac{1}{18} \]

6. Convert \(1\) to a fraction with a denominator of \(18\): \[ 1 = \frac{18}{18} \]

7. Now perform the subtraction: \[ \frac{18}{18} - \frac{1}{18} = \frac{18 - 1}{18} = \frac{17}{18} \]

Thus, the equivalent expression is: \[ \boxed{\frac{17}{18}} \]