Evaluate the expression.

Question

-3 to the -1 power + 4 to the -2 power

Answer 1

To evaluate the expression, we need to calculate each exponent separately and then add the results together.

First, let's calculate -3 to the -1 power:
(-3)^(-1) = 1/(-3) = -1/3

Next, let's calculate 4 to the -2 power:
4^(-2) = 1/(4^2) = 1/16

Now, let's add the two results together:
-1/3 + 1/16

To add these fractions, we need a common denominator, which is 48.

Multiplying the numerator and denominator of -1/3 by 16, we get:
(-1/3) * (16/16) = -16/48

The expression now becomes:
-16/48 + 1/16

To add these fractions, we need to have the same denominator, which is 48.

Multiplying the numerator and denominator of 1/16 by 3, we get:
(1/16) * (3/3) = 3/48

Now, the expression becomes:
-16/48 + 3/48

Combining these fractions, we get:
(-16 + 3)/48 = -13/48

Therefore, the evaluated expression is -13/48.