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

Question

(4 points)

(2 ^ 6 * 2 ^ 4)/(2 ^ 8)

= (- 2) ^ - 8 * (- 2) ^ 11

1/(x ^ - 1)

(1/2) ^ - 3

Answer 1

To compare the simplifed expressions and order them from least to greatest on the number line, we need to evaluate each expression.

Let's evaluate each expression:

(2 ^ 6 * 2 ^ 4) / (2 ^ 8) can be simplified using the exponent rule: a ^ m * a ^ n = a ^ (m + n).

So, (2 ^ 6 * 2 ^ 4) / (2 ^ 8) = 2 ^(6 + 4 - 8) = 2 ^ 2 = 4.

Next, let's simplify (- 2) ^ - 8 * (- 2) ^ 11 using the exponent rule: a ^ - m = 1 / a ^ m.

So, (- 2) ^ - 8 * (- 2) ^ 11 = 1 / ((- 2) ^ 8) * (- 2) ^ 11 = - 2 ^ - 8 * (- 2) ^ 11 = - 1 / (2 ^ 8) * (- 2) ^ 11 = (- 1 / 256) * (- 2) ^ 11 = (- 1 / 256) * (- 2048) = 2048 / 256 = 8.

Next, let's simplify 1 / (x ^ - 1). To simplify this expression, we need to use the exponent rule: a ^ - m = 1 / a ^ m.

So, 1 / (x ^ - 1) = 1 / (1 / x) = x.

Next, let's simplify (1/2) ^ - 3. To simplify this expression, we need to use the exponent rule: a ^ - m = 1 / a ^ m.

So, (1/2) ^ - 3 = 1 / ((1/2) ^ 3) = 1 / (1/8) = 8.

Now, let's order the simplifed expressions from least to greatest: 4, 8, x, 8.

Based on the given information, it is not possible to determine the order of the expressions on the number line without knowing the specific value of x.