How to subtract exponents - ACT Math
Card 0 of 7
Reduce 
to simplest form.
Reduce
When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.
becomes 
,
becomes 
,
and 
stays the same because there is no other z term to combine with it.
Thus resulting in:
When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.
and
Thus resulting in:
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Simplify: 32 * (423 - 421)
Simplify: 32 * (423 - 421)
Begin by noting that the group (423 - 421) has a common factor, namely 421. You can treat this like any other constant or variable and factor it out. That would give you: 421(42 - 1). Therefore, we know that:
32 * (423 - 421) = 32 * 421(42 - 1)
Now, 42 - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:
32 * 421(42 - 1) = 32 * 421(3 * 5)
Combining multiples withe same base, you get:
33 * 421 * 5
Begin by noting that the group (423 - 421) has a common factor, namely 421. You can treat this like any other constant or variable and factor it out. That would give you: 421(42 - 1). Therefore, we know that:
32 * (423 - 421) = 32 * 421(42 - 1)
Now, 42 - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:
32 * 421(42 - 1) = 32 * 421(3 * 5)
Combining multiples withe same base, you get:
33 * 421 * 5
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Simplify. Leave no negative exponents in the final answer.
Simplify. Leave no negative exponents in the final answer.
The first step in the problem is to combine like terms in the numerator, remembering that 
:
Next, we resolve the numerator, using 
and 
:
Lastly, simplify the negative exponent using 
Thus,
The first step in the problem is to combine like terms in the numerator, remembering that
Next, we resolve the numerator, using
Lastly, simplify the negative exponent using
Thus,
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Simplify to remove fractions:
Simplify to remove fractions:
The first step is to simplify each fraction by dividing like terms, remembering that 
, to get:
Next, combine using multiplication and the rule 
:
Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.
So,
The first step is to simplify each fraction by dividing like terms, remembering that
Next, combine using multiplication and the rule
Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.
So,
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can be written as which of the following?
A. 
B. 
C. 
A.
B.
C.
A is not equivalent because exponents in denominators mean subtraction of exponents and not division of them. Furthermore, A, when computed, comes out to 
instead of 
.
B is equivalent by the aforementioned exponential property, while C is simply computing the expression.
A is not equivalent because exponents in denominators mean subtraction of exponents and not division of them. Furthermore, A, when computed, comes out to
B is equivalent by the aforementioned exponential property, while C is simply computing the expression.
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Simplify the following: 
Simplify the following:
When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are 
and 
. When subtracted, the result is 
. Thus, the correct answer is 
.
When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are
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Simplify: 
Simplify:
When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer.
In this case, subtract 
from 
. That yields 
as the new exponent and 
as the answer.
When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer.
In this case, subtract
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