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

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.

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

Next, expand the denominator.

Simplify by canceling terms.

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

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

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.

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

Now, let’s combine the following:

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

Also, we divide the coefficients like normal.

So, we get

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

Now, let’s divide the following:

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 .