Rational Number Properties and Simplification

In this problem, we need to simplify a product of four rational numbers and express the result in standard form.

Let's write down the expression from part a. We have negative thirty-six times negative thirty-five over seventy-six, times nineteen over fifteen, times three over negative two raised to the power of negative one.

First, let's deal with the term that has a negative exponent. Recall that a fraction raised to the power of negative one is simply its reciprocal.

So, three over negative two raised to the power of negative one becomes negative two over three.

Now, let's multiply these terms together. We can combine them into a single fraction. For the signs, we have three negative signs, so the product will be negative.

Next, let's look for common factors to simplify before multiplying. Notice that seventy-six is equal to four times nineteen.

We can cancel out the factor of nineteen from the numerator and the denominator.