Multiplying and Dividing Exponents - Math
Card 0 of 772
Simplify the following expression.
Simplify the following expression.
When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: 
.
In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.
Now, simplifly the numerals.
When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example:
In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.
Now, simplifly the numerals.
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Solve for 
: 
Solve for
Rewrite each side of the equation to only use a base 2:
The only way this equation can be true is if the exponents are equal.
So:
The 
on each side cancel, and moving the 
to the left side, we get:
Rewrite each side of the equation to only use a base 2:
The only way this equation can be true is if the exponents are equal.
So:
The
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Simplify the expression:
Simplify the expression:
First simplify the second term, and then combine the two:
First simplify the second term, and then combine the two:
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Simplify the following expression.
Simplify the following expression.
We are given: 
.
Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.
Thus, we have 
.
We are given:
Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.
Thus, we have
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Simplify the following expression.
Simplify the following expression.
Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.
Thus, we have 
.
We also recall that for negative exponents,
.
Thus, 
.
Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.
Thus, we have
We also recall that for negative exponents,
Thus,
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Simplify the following exponent expression:
Simplify the following exponent expression:
Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:
Multiply the exponents:
Simplify:
Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:
Multiply the exponents:
Simplify:
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Simplify 
Simplify
First, combine exponents of like variables. This gives us 
First, combine exponents of like variables. This gives us
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Simplify 
Simplify
First, combine exponents of like variables. This gives us 
which simplifies to 
First, combine exponents of like variables. This gives us
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Simplify.
Simplify.
When multiplying exponents with the same base, you just have to add the exponents.
When multiplying exponents with the same base, you just have to add the exponents.
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Simplify.
Simplify.
When dividing exponents with the same base, we just subtract the exponents.
When dividing exponents with the same base, we just subtract the exponents.
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Simplify.
Simplify.
When dividing exponents with the same base, we just subtract the exponents.
When dividing exponents with the same base, we just subtract the exponents.
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Simplify: 
Simplify:
When dividing exponents with the same base, we subtract the exponents and keep the base the same.
When dividing exponents with the same base, we subtract the exponents and keep the base the same.
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Simplify: 
Simplify:
When multiplying exponents with the same base, we add the exponents and keep the base the same.
When multiplying exponents with the same base, we add the exponents and keep the base the same.
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Simplify: 
Simplify:
When multiplying exponents with the same base, we add the exponents and keep the base the same.
When multiplying exponents with the same base, we add the exponents and keep the base the same.
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Simplify: 
Simplify:
When multiplying exponents with the same base, we add the exponents and keep the base the same.
When multiplying exponents with the same base, we add the exponents and keep the base the same.
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Simplify: 
Simplify:
When multiplying exponents with the same base, we just keep the base the same and add the exponents.
When multiplying exponents with the same base, we just keep the base the same and add the exponents.
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Simplify: 
Simplify:
When multiplying exponents with the same base, we just keep the base the same and add the exponents.
When multiplying exponents with the same base, we just keep the base the same and add the exponents.
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Simplify the following expression
Simplify the following expression
Remember that any number raised to the 0th power equals 1
Remember that any number raised to the 0th power equals 1
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Evaluate:
Evaluate:
When multiplying with same base but different exponents, you just add the exponents and keep the base the same.
When multiplying with same base but different exponents, you just add the exponents and keep the base the same.
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Simplify this expression:
Simplify this expression:
When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:
For the above problem,
Therefore, the expression simplifies to:
When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:
For the above problem,
Therefore, the expression simplifies to:
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