How to divide exponential variables - ISEE Upper Level: Quantitative Reasoning

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

Break the fraction up and apply the quotient of powers rule:

To simplify this expression, look at the like terms separately. First, simplify . This becomes . Then, deal with the . Since the bases are the same and you're dividing, you can subtract exponents. This gives you Since the exponent is positive, you put in the numerator. This gives you a final answer of .

A negative number raised to an odd power is negative; a negative number raised to an even power is positive. It follows that is negative and is positive. Also, the reciprocal of a nonzero number assumes the same sign as the number itself, so the reciprocal of is positive and that of is negative. It follows that the reciprocal of is the greater of the two.

Break the fraction up and apply the quotient of powers rule:

To divide a variable with an exponent, you can write out all the multiplies, which for this question would look like:

Then cancel out the matching p's, leaving:

Or, if the top and bottom are the same variable, you can simply subtract the bottom exponent from the top exponent.

To divide variables with exponents, either:

Write out the multiplies, then reduce

or subtract the bottom exponent from the top, like so

Remember, negative exponent means dividing. would also be correct, but you should know that is equivalent to

Start by factoring the numerator. can be removed from each term.

Next, expand the denominator.

Simplify by canceling terms.

In the denominator, apply the exponent to the terms in parentheses.

Terms with negative exponents can be inverted within the fraction to eliminate the negative.

Simplify by canceling variables and mulitplying.

Break up the fraction into components with like-terms.

Simplify by combining exponents. Remember that exponents in the denominator will become negative.

Finally, put any negative exponent terms into the denominator.

To divide variables with exponents, we will use the following formula:

Now, let’s combine the following:

When dividing variables, we can only divide like variable.

Also, when dividing variables with exponents, we subtract the exponents. In other words:

So, we get

To simplify, we will use the following formula:

So, given the problem, we get

To divide like terms with exponents, we will use the following formula:

So, we get

To divide like variables with exponents, we will use the following formula:

So, we get

To divide like variables with exponents, we will use the following formula:

Also, we divide the coefficients like normal.

So, we get