In the first quotient, divide 12 and 3 by the GCF (3). In the second quotient, divide 6 and 30 by the GCF (6). You could also divide all the intergers by 2, but it would take longer to simplify since you would end up with larger numbers.

Organize the variables so like terms are together in the numerator and in the denominator. Then use rules of exponents to combine  and  and  and  and  and  in the numerator. Remember the following exponent rule: , 

Since  is in the numerator and the denominator, you can cancel it out.

Use the exponent rule  to further simplify the expression by combining the terms  and  and  and .

First, organize the variables so like terms are together in the numerator and in the denominator.

Second, use rules of exponents to combine the following terms: and , and , and and . Remember the following exponent rules:

Third, divide the 2 and the 4 by the GCF, 2.

Divide 6 and 24 by 6 (the GCF) and 14 and 21 by 7 (the GCF). Combine like terms in the numerator and the denominator.

Use rules of exponents to combine the following terms: and and and  Remember the following exponent rules:

and

Combine like terms in the numerator and the denominator. Then, divide 20 and 5 by 5 (the GCF). 

The GCF rule can also be used to remove from the numerator and the deonominator. goes into once.

Use rules of exponents to combine the terms and . Remember the following exponent rules:

In the first quotient, divide 6 and 8 by the GCF (2). In the second quotient, divide 4 and 20 by the GCF (4).

Organize the variables so like terms are together in the numerator and in the denominator. Then use rules of exponents to combine  and  and  and  in the numerator. Remember the following exponent rule: 

Use the rules of exponents 

and 

to further simplify the expression by combining the terms and , and and .

First, in the first quotient, divide 27 and 9 by the GCF (9). In the second quotient, divide 20 and 16 by the GCF (4).

Second, organize the variables so like terms are together in the numerator and in the denominator.

Third, multiply the integers and use the rules of exponents to combine the following terms: and , and , and and . Remember the following exponent rule: , 

Fourth, use the rules of exponents

and

to further simplify the expression by combining the terms and  and  and .

Because 28 and 12, the coefficients in the second quotient, share common factors, you can divide them by the GCF (4). Because the cofficients in the first quotient are technically 1 and 8, you cannot further reduce the 8.

Organize the variables so like terms are together in the numerator and in the denominator. Then, multiply  and  in the denominator and  use rules of exponents to combine  and  in the numerator. Remember the following exponent rule: , 

Use the exponent rule 

to further simplify the expression by combining the terms  and  and  and .

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

Now use the quotient rule on the variables by subtracting exponents:

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators, by dividing 9 and 3 each by 3:

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable and exponent to the denominator to make it positive: