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When working with fractions, it's important to understand the roles of the numerator and the denominator.

The numerator is the top number in a fraction and it represents how many parts of a whole or group are being considered.
For example, in the fraction \(\frac{-80}{-10}\), \-80\ is the numerator.
The denominator, on the other hand, is the bottom number and it shows the total number of equal parts.
In the same fraction, \-10\ is the denominator.

Knowing this distinction helps in breaking down and simplifying complex fractions.
Whenever you simplify fractions, you work on both the numerator and the denominator separately before combining them back.

This ensures accuracy and makes the steps more manageable.

Fraction simplification involves reducing the fraction to its simplest form.

To do this, you divide both the numerator and the denominator by their greatest common divisor (GCD).

In our example, we eventually get the fraction \(\frac{-80}{-10}\).
Both \-80\ and \-10\ can be evenly divided by \-10\, their greatest common divisor.

When you divide both, you end up with \(\frac{80}{10}= 8\).

This fraction \(8\) is in its simplest form.

Always look for common factors between the numerator and the denominator.
This makes the fraction simpler and easier to work with.
Simplified fractions also make it easier to compare and understand values.

Exponentiation is the process of raising a number to a power.
This means you multiply the number by itself a certain number of times.
For example, \(2^{3}\) means multiplying 2 by itself three times: \(2 \times 2 \times 2 = 8\).

In our exercise, we see multiple instances of exponentiation:
\((-4)^{3}\) and \(-2^{3}\).

For \((-4)^{3}\), you multiply \-4\ by itself three times, resulting in \(-64\).
Similarly, \(-2^{3}\) simplifies to \-8\.

Understanding how exponentiation works helps you accurately simplify expressions.
It ensures that you don't make mistakes in the calculations down the line.


Remember, always simplify exponents before moving on to other operations.
This creates a solid foundation for solving the rest of the problem.