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Example Questions
Example Question #1 : How To Multiply Monomial Quotients
Simplify:
Since there are no like terms in the numerator or in the denominator, you can only combine ther terms on the numerator and denominator so that they are in one quotient.
Use the rules of exponents and
to further simplify the expression by combining the terms
and
,
and
, and
and
.
Example Question #2 : How To Multiply Monomial Quotients
Simplify:
Divide both integers 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:
,
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
.
Example Question #3 : How To Multiply Monomial Quotients
Simplify:
Divide both 4 and 2 by the GCF (2) and organize the variables so like terms are together in the numerator and in the denominator. Multiply the integers 4 and 3 together.
Then use rules of exponents to combine and
and
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
.
Example Question #4 : How To Multiply Monomial Quotients
Simplify:
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
.
Example Question #5 : How To Multiply Monomial Quotients
Simplify:
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.
Example Question #1 : How To Multiply Monomial Quotients
Simplify:
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
Example Question #7 : How To Multiply Monomial Quotients
Simplify:
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:
Example Question #1 : How To Multiply Monomial Quotients
Simplify:
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
.
Example Question #1 : How To Multiply Monomial Quotients
Simplify:
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
.
Example Question #10 : How To Multiply Monomial Quotients
Simplify:
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
.
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