is the multiplicative inverse of , so, by definition, . We show that this is insufficient information, however, with two cases.

Case 1:

Case 2:

Therefore,it is not clear which, if either, is the greater, or 1.

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square first.

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:

Now, since all of the variables are positive powers, this is easy. Normally, you would begin by reducing the numeric coefficient. This is not necessary since there is only a 5 in the numerator. Therefore, combine the like variables first:

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

If Jack and Jenny paint the vases together, they will paint 5 vases per hour since Jack's rate of painting is 3 vases per hour, while Jenny's rate is 2 vases per hour.

If there are 30 vases to paint, and they paint 5 vases per hour, it will take 6 hours to paint all the vases because 30 divided by 5 is 6.

To solve separate each part of the terms and divide. When dividing variables with exponents, subtract the exponents.

Simplify the following expression:

When we are dividing variables, we can simpligy by subtracting the exponent of the variable on bottom from the variable on the top.

So because t has an exponent of 4 on top and 2 on the bottom, the new exponent will be:

Do the same for our other two exponents (x and p) to get the following

Making our answer:

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:

Next, go ahead and reduce the numeric coefficient:

Then, combine the like variables first:

Finally, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

Factors are multiplied together to reach a specific target number. When you divide a target number by one of its factors, the result is always a whole number.

In this case, we can evaluate the numbers that can be multiplied to get 56.

12 is not a factor of 56. When you divide 56 by 12, the answer is not a whole number.

For this division problem, you must deal with the like terms.

You will divide the constants and then divide the variables.

and then

because when dividing exponents with common bases, you just subtract the exponents.

The variable remains unchanged and your answer is,

.

When dividing by variables you must deal with the like variables first.

Since there are variables on the numerator and denominator, you would divide them together.

The constants will divide regularly and the variables will cancel out

.

The other variables are left alone so the final answer will just be

.