Introduction:
To find the number that should be multiplied to (-8)^-3 to get (-6)^-3, we need to understand the concept of exponentiation and how negative exponents are related to reciprocals. In this explanation, we will break down the steps to solve this problem.

Step 1: Understanding Exponentiation:
Exponentiation is a mathematical operation that involves raising a number to a certain power. For example, in the expression x^n, x is the base and n is the exponent. It means multiplying x by itself n times.

Step 2: Negative Exponents and Reciprocals:
When a number is raised to a negative exponent, it signifies taking the reciprocal of that number raised to the positive exponent. In other words, if x is a non-zero number, then x^-n is equal to 1/(x^n).

Step 3: Finding the Number:
To find the number that should be multiplied to (-8)^-3 to get (-6)^-3, we can use the property of reciprocals. Since (-8)^-3 is the reciprocal of (-8)^3 and (-6)^-3 is the reciprocal of (-6)^3, we need to find the ratio of these two reciprocals.

Step 4: Calculating the Ratio:
Let's calculate the ratio by dividing the reciprocal of (-8)^3 by the reciprocal of (-6)^3.

((-8)^-3) / ((-6)^-3) = ((1/(-8)^3) / (1/(-6)^3))

Step 5: Simplifying the Ratio:
Simplifying the ratio, we get:

((-8)^-3) / ((-6)^-3) = ((1 / (-8)^3) * ((-6)^3 / 1))

Step 6: Evaluating the Exponents:
Evaluating the exponents, we have:

((-8)^-3) / ((-6)^-3) = ((1 / (-512)) * ((-216) / 1))

Step 7: Calculating the Value:
Calculating the value, we get:

((-8)^-3) / ((-6)^-3) = (-1 / 512) * (-216) = 216 / 512 = 27 / 64

Therefore, the number that should be multiplied to (-8)^-3 to get (-6)^-3 is 27/64.

Conclusion:
In conclusion, to find the number that should be multiplied to (-8)^-3 to get (-6)^-3, we used the concept of negative exponents and reciprocals. By simplifying the ratio of the reciprocals and evaluating the exponents, we found that the number is 27/64.