How to subtract exponents - ISEE Upper Level Quantitative Reasoning
Card 1 of 52
Simplify:
Simplify:
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In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
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Evaluate:
Evaluate:
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In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
Now they must be multiplied out before they can be added:
In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
Now they must be multiplied out before they can be added:
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Define an operation 
as follows:
For all real numbers 
,
.
Evaluate: 
.
Define an operation
For all real numbers
Evaluate:
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Subtract and simplify:
Subtract and simplify:
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Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
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Subtract and simplify:
Subtract and simplify:
Tap to reveal answer
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
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Define an operation as follows:
For all real numbers ,
.
Evaluate: 
.
Define an operation
For all real numbers
Evaluate:
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, so
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Define an operation as follows:
For all real numbers ,
.
Evaluate: 
Define an operation
For all real numbers
Evaluate:
Tap to reveal answer
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Define 
as follows:
Evaluate 
.
Define
Evaluate
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Simplify the expresseion:
Simplify the expresseion:
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Variable terms can be combined by adding and subtracting if and only of they are like - that is, if each exponent of each variable is the same. In the given expression, no two exponents are the same. The terms cannot be combined, and the expression is already simplified.
Variable terms can be combined by adding and subtracting if and only of they are like - that is, if each exponent of each variable is the same. In the given expression, no two exponents are the same. The terms cannot be combined, and the expression is already simplified.
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Define a function 
as follows:
Evaluate 
.
Define a function
Evaluate
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Define a function 
.
Evaluate 
Define a function
Evaluate
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Define 
and 
.
Evaluate 
.
Define
Evaluate
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, by definition, so
Evaluate 
and 
separately:
Evaluate
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Define 
as follows:
Evaluate 
.
Define
Evaluate
Tap to reveal answer
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Simplify:
Simplify:
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In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
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Evaluate:
Evaluate:
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In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
Now they must be multiplied out before they can be added:
In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:
Now they must be multiplied out before they can be added:
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Define an operation as follows:
For all real numbers ,
.
Evaluate: .
Define an operation
For all real numbers
Evaluate:
Tap to reveal answer
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Subtract and simplify:
Subtract and simplify:
Tap to reveal answer
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
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Subtract and simplify:
Subtract and simplify:
Tap to reveal answer
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
Consider a vertical subtraction process:
Rewrite as the addition of the opposite of the second expression, as follows:
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Define an operation as follows:
For all real numbers ,
.
Evaluate: .
Define an operation
For all real numbers
Evaluate:
Tap to reveal answer
, so
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Define an operation as follows:
For all real numbers ,
.
Evaluate:
Define an operation
For all real numbers
Evaluate:
Tap to reveal answer
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