Put the simplified expressions in order on the number line from least to greatest.
1/(4^-2)
(-2)^-8 x (-2)^11
(2^6 - 2^4)/2^2
(1/2)^-3
To order the simplified expressions from least to greatest on the number line, we need to calculate the values of each expression.
1. Simplifying 1/(4^-2):
Recall that a negative exponent is equivalent to taking the reciprocal. So, 4^-2 is equal to 1/(4^2) = 1/16.
2. Simplifying (-2)^-8 x (-2)^11:
Remember that when multiplying two powers with the same base, we add their exponents. Therefore, (-2)^-8 x (-2)^11 is equal to (-2)^(-8 + 11) = (-2)^3 = -8.
3. Simplifying (2^6 - 2^4)/2^2:
Working out the exponents, we have (2^6 - 2^4)/2^2 = (64 - 16)/4 = 48/4 = 12.
4. Simplifying (1/2)^-3:
Again, recall that a negative exponent is equivalent to taking the reciprocal. So, (1/2)^-3 is equal to 2^3 = 8.
Now, let's order the expressions from least to greatest using their calculated values:
1/16 < 8 < 12 < -8
The order on the number line will be:
-8, 1/16, 8, 12