Question

put the simplified expressions in order from least to greatest on a number line that contains negative and positive numbers that both go to 10 and -10 on each side.


2^6 - 2^4 / 2^2

1/4^-2

(-2)^-8 x (-2)^11

(1/2)^-3

Answer 1

Let's simplify each expression step by step.

1. **Simplifying \(2^6 - 2^4 / 2^2\)**

First, apply the order of operations:
\[
2^6 - \frac{2^4}{2^2}
\]

Calculate \(\frac{2^4}{2^2} = 2^{4-2} = 2^2 = 4\):

Now substitute back into the expression:
\[
2^6 - 4
\]
Calculate \(2^6 = 64\):
\[
64 - 4 = 60
\]

So, the result is **60**.

2. **Simplifying \(\frac{1}{4^{-2}}\)**

Using the property of exponents, we have:
\[
\frac{1}{4^{-2}} = 4^{2} = 16
\]

So, the result is **16**.

3. **Simplifying \((-2)^{-8} \times (-2)^{11}\)**

Use the property of exponents:
\[
(-2)^{-8} \times (-2)^{11} = (-2)^{-8+11} = (-2)^3
\]

Calculate \((-2)^3 = -8\).

So, the result is **-8**.

4. **Simplifying \((\frac{1}{2})^{-3}\)**

Using the property of exponents:
\[
\left(\frac{1}{2}\right)^{-3} = 2^{3} = 8
\]

So, the result is **8**.

Now, we have the simplified values:
- \(2^6 - 2^4 / 2^2 = 60\)
- \(\frac{1}{4^{-2}} = 16\)
- \((-2)^{-8} \times (-2)^{11} = -8\)
- \((\frac{1}{2})^{-3} = 8\)

Putting these values in order from least to greatest:
1. **-8**
2. **8**
3. **16**
4. **60**

Therefore, the final order from least to greatest is:
\[
-8, 8, 16, 60
\]