Put the simplified expressions in order on the number line from least to greatest.

Question

(-2)^-8.(2)^11

(1/2)^-3

2^6 -2^4/2^2

1/4^-2

Answer 1

To simplify the expressions given, let's evaluate each one step by step.

1. For \((-2)^{-8} \cdot (2)^{11}\): \[ (-2)^{-8} = \frac{1}{(-2)^8} = \frac{1}{256} \] \[ (2)^{11} = 2048 \] Thus, \[ (-2)^{-8} \cdot (2)^{11} = \frac{1}{256} \cdot 2048 = \frac{2048}{256} = 8 \]

2. For \(\left(\frac{1}{2}\right)^{-3}\): \[ \left(\frac{1}{2}\right)^{-3} = 2^3 = 8 \]

3. For \(2^6 - \frac{2^4}{2^2}\): \[ 2^6 = 64, \] \[ \frac{2^4}{2^2} = 2^{4-2} = 2^2 = 4 \] Thus, \[ 2^6 - \frac{2^4}{2^2} = 64 - 4 = 60 \]

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

Now we have the simplified values:

• \((-2)^{-8} \cdot (2)^{11} = 8\)
• \(\left(\frac{1}{2}\right)^{-3} = 8\)
• \(2^6 - \frac{2^4}{2^2} = 60\)
• \(\frac{1}{4^{-2}} = 16\)

Putting these values in order from least to greatest:

• 60
• 16
• 8
• 8

So, if we order everything from least to greatest:

1. \(60\)
2. \(16\)
3. \(8\)
4. \(8\)

The final order from least to greatest is:

• \(60\)
• \(16\)
• \(8\)
• \(8\) (but both are the same, so they can be grouped)

Thus, the final presentation would be:

1. \(60\)
2. \(16\)
3. \(8\) (doubled)

If you need them uniquely, \(60 < 16 < 8\).