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When simplifying numerical expressions, it's important to understand how to evaluate exponents correctly. An exponent tells you how many times to multiply a number by itself. In our exercise, we are dealing with negative numbers raised to exponents.

To calculate \((-2)^3\), you multiply \(-2\) by itself three times. Each multiplication maintains the negative sign, because multiplying a negative number an odd number of times results in a negative number. So, \((-2) \times (-2) = 4\) and then \(4 \times (-2) = -8\).

For \((-1)^4\), we multiply \(-1\) by itself four times. Since the exponent is even, the result will always be positive. Following this, \((-1) \times (-1) = 1\) twice, so raising \(-1\) to the fourth power results in \(1\). Using these principles ensures that you evaluate exponents correctly and avoid errors in further calculations.

Once you've evaluated the exponents, the next step involves applying the constants. Constants are the numbers that multiply the result of your exponents.

For our exercise, we apply these constants to the results of the exponent evaluations from the previous step. We first multiply 4 by \((-2)^3\), which we found equals \(-8\). Multiply these together to get \(4 \times (-8) = -32\).

Similarly, apply \(-3\) to the result of \((-1)^4\), which equals \(1\). So, you have \(-3 \times 1 = -3\).

Applying constants means scaling the effect of your base expression by the magnitude of the constant. This step integrates the results of the exponents with the overall expression. Understanding this process is key to accurate simplification.

The final step in simplifying our numerical expression is to combine the terms computed in the constants application. Combining terms means performing the arithmetic operations to reduce the expression to a single number.

In this exercise, you need to add the two results from the constants application step: \(-32\) and \(-3\). The operation \(-32 + (-3)\) results in \(-35\).

Adding negative numbers is similar to adding positive ones, except you move in the negative direction on the number line. Always be mindful of the signs to prevent mistakes. Combining terms is the essential final touch in simplifying expressions accurately. It's the summing of all previous steps' efforts into one neat solution.