Final answer:
The exponent for the expression 1/8 x 1/8 is 8^-2. Each 1/8 is written as 8^-1, and when squaring, you multiply the exponent by 2, resulting in 8^-2.
Step-by-step explanation:
When you multiply 1/8 by 1/8, you are essentially squaring the fraction 1/8. In terms of exponents, 1/8 can be written as 8-1. Therefore, when you square 1/8, you take the exponent of -1 and multiply it by 2, because you are squaring the expression. So, squaring 1/8 would result in 8-2, which is the exponent for the expression 1/8 x 1/8.
Squaring of exponentials typically means you square the digit term as usual, and multiply the exponent by 2. Converting the exponents to the same value and performing the mathematical operations is a standard process whether dealing with positive or negative exponents. For example, if you were working with 2.4 x 10-2 and moved the decimal point twice to the left, you would get the correct answer of 0.024.