To divide two numbers of like sign, just divide their absolute values; their quotient will be positive.

Dividing with a negative is the same as multiplying with a negative. You only have the number be negative if the one of the numbers is negative and the other is positive. If both numbers are negative, then they will cancel each other and be positive.

Here we can see that we have one negative and one positive, and respectively. This means that our final answer will have a negative in it.

Divide the problem as you would, making sure that you place a negative sign in your answer.

Our answer is .

Since absolute value bars are grouping symbols, we first raise to the power of 3. An odd power of a negative number is negative, so we do this by raising 5 to the third power, then affixing a negative symbol.

The absolute value of a negative number is the corresponding positive, so

.

Evaluate the terms of the inner parentheses.

Double negatives translates to a positive sign.

The answer is:

Substitute for in the expression.

The absolute value of a nonnegative number is the number itself; the absolute value of a negative number can be obtained by removing the negative symbol. Therefore,

and .

This makes the statements and both equivalent to the statement , which is false.

This also makes the statement equivalent to , which is the only true statement of the three.

To subtract with negative numbers, change to an addition and make the second number its opposite:

To add two numbers of unlike sign, if the positive has the greater absolute value, simply subtract the absolute values.

The answer is 45.

When a negative number is multipied by a positive number, the result is negative.

Therefore,

.

To find the value of , plug in the given x and y values into the appropriate places.

For and ,

Now, follow the order of operations to simplify. Tackle the exponent first.

Next, multiply.

Finally, subtract.