Sum of multiplicative and additive inverse of 2^-3

To find the sum of the multiplicative and additive inverses of 2^-3, we first need to understand what these terms mean.

Multiplicative Inverse:
The multiplicative inverse of a number is the value that, when multiplied by the original number, gives a product of 1. For any non-zero number a, its multiplicative inverse is denoted as 1/a.

In this case, we need to find the multiplicative inverse of 2^-3. To do this, we can rewrite 2^-3 as 1/(2^3). The exponent of -3 means that we need to take the reciprocal of 2^3.

Additive Inverse:
The additive inverse of a number is the value that, when added to the original number, gives a sum of 0. For any number a, its additive inverse is denoted as -a.

Now, let's calculate the multiplicative and additive inverses of 2^-3:

Multiplicative Inverse of 2^-3:
To find the multiplicative inverse of 2^-3, we need to take the reciprocal of 2^3. The reciprocal of a number is obtained by switching the numerator and denominator.

So, the multiplicative inverse of 2^-3 is 1/(2^3) = 1/8.

Additive Inverse of 2^-3:
To find the additive inverse of 2^-3, we need to change the sign of 2^-3. Since 2^-3 is a positive number, its additive inverse will be -2^-3.

Sum of Multiplicative and Additive Inverse:
Finally, we can find the sum of the multiplicative and additive inverses of 2^-3 by adding the values we calculated earlier.

Sum = (1/8) + (-2^-3)

Simplifying this expression:

Sum = 1/8 - 1/8

Sum = 0

Therefore, the sum of the multiplicative and additive inverses of 2^-3 is 0.