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Exponents are a way to express repeated multiplication of a number by itself. In the expression \((3)^2\), the exponent "2" indicates that the base number "3" is multiplied by itself. So, \((3)^2 = 3 \times 3 = 9\).

With negative numbers, the exponent's impact depends on whether it is odd or even. For example, \((-2)^3\) shows that \(-2\) is multiplied by itself three times: \(-2 \times -2 \times -2\). First, \(-2 \times -2 = 4\), and then \(4 \times -2 = -8\). Here, the result is negative because multiplying a negative number an odd number of times yields a negative number.

In the case of \((-1)^5\), the multiplication goes like this: \((-1)\) multiplied five times stays \(-1\) because each pair of negatives results in a positive, but one lone negative remains due to the odd number of factors.

Once the exponents are simplified, it's time to handle multiplication and distribution. This step involves multiplying the numbers outside the parentheses with the results inside. We start with the expression \(-2 \times (3)^2\).

Here, \((3)^2\) simplifies to 9, so multiply \(-2\) by 9 to get \(-18\).

• \(-2 \times 9 = -18\)

Next, tackle \(-2 \times (-2)^3\). After simplifying \((-2)^3\) to \'-8\', multiply \(-2\) by \'-8\' to produce \(16\).

• \(-2 \times (-8) = 16\)

Lastly, for the expression \(-6 \times (-1)^5\), we see \((-1)^5 = -1\), so multiply \(-6\) by \'-1\' to get \'6\'.

• \(-6 \times (-1) = 6\)

It is crucial to follow the correct order when performing operations to arrive at the accurate solution. Often referred to by the acronym "PEMDAS" (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this order ensures consistency in results.

In our expression \(-2(3)^2-2(-2)^3-6(-1)^5\), we first simplified the exponents as described and then dealt with multiplication. Each of these operations comes before any addition or subtraction, which occurs next.

Finally, we combine or add the results from each multiplication:

• First, add \(-18 + 16 = -2\)
• Then, add \(-2 + 6 = 4\)

This methodical approach ensures that the final result is both logical and precise.