How to subtract exponents - SAT Math
Card 0 of 13
If m and n are integers such that m < n < 0 and _m_2 – _n_2 = 7, which of the following can be the value of m + n?
I. –5
II. –7
III. –9
If m and n are integers such that m < n < 0 and _m_2 – _n_2 = 7, which of the following can be the value of m + n?
I. –5
II. –7
III. –9
m and n are both less than zero and thus negative integers, giving us _m_2 and _n_2 as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.
m and n are both less than zero and thus negative integers, giving us _m_2 and _n_2 as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.
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If 
, then what is 
?
If
Follow the order of operations by solving the expression within the parentheses first.
Return to solve the original expression.
Follow the order of operations by solving the expression within the parentheses first.
Return to solve the original expression.
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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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Solve:
Solve:
Subtract the denominator exponent from the numerator's exponent, since they have the same base.
Subtract the denominator exponent from the numerator's exponent, since they have the same base.
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To simplify, we can rewrite the numerator using a common exponential base.
Now, we can factor out the numerator.
The eights cancel to give us our final answer.
To simplify, we can rewrite the numerator using a common exponential base.
Now, we can factor out the numerator.
The eights cancel to give us our final answer.
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Simplify the following expression:
Simplify the following expression:
The correct answer can be found by subtracting exponents that have the same base. Whenever exponents with the same base are divided, you can subtract the exponent of the denominator from the exponent of the numerator as shown below to obtain the final answer:
You do not do anything with the y exponent because it has no identical bases.
The correct answer can be found by subtracting exponents that have the same base. Whenever exponents with the same base are divided, you can subtract the exponent of the denominator from the exponent of the numerator as shown below to obtain the final answer:
You do not do anything with the y exponent because it has no identical bases.
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Evaluate 
Evaluate
When subtracting exponents, we don't multiply the exponents but we try to factor to see if we simplify the subtraction problem. In this case, we can simplify it by factoring 
. We get 
.
When subtracting exponents, we don't multiply the exponents but we try to factor to see if we simplify the subtraction problem. In this case, we can simplify it by factoring
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Evaluate 
Evaluate
Although we have different bases, we know that 
. As long as exponents are the same, you are allowed to break the base to its prime numbers. Next, we can factor 
. 
Although we have different bases, we know that
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Evaluate 
Evaluate
Although we have different bases, we know that 
. Therefore our expression is 
. Remember to apply the power rule of exponents. Next, we can factor out 
We get 
.
Although we have different bases, we know that
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Simplify so that all exponents are positive:
Simplify so that all exponents are positive:
When we divide two polynomials with exponents, we subtract their exponents.
Remember that the question asks that all exponents be positive numbers. Therefore:
When we divide two polynomials with exponents, we subtract their exponents.
Remember that the question asks that all exponents be positive numbers. Therefore:
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Evaluate:
Evaluate:
When subtracting with exponents, we try to factor out some terms.
We can factor out 
to get
.
When subtracting with exponents, we try to factor out some terms.
We can factor out
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Evaluate:
Evaluate:
When subtracting with exponents, we try to factor out some terms.
We can factor out 
to get
.
When subtracting with exponents, we try to factor out some terms.
We can factor out
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Simplify:
Simplify:
Although we have different bases, we know that 
.
Therefore,
.
Finally, we factor out 
to get
.
Although we have different bases, we know that
Therefore,
Finally, we factor out
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