Consider (2x)4. In this case we are taking the entire product inside the parentheses to the 4th power.
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(2x)4 = (2x)((2x)(2x)(2x) |
Definition of the exponent 4 |
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= (2 · 2 · 2 · 2)(x · x · x · x) |
Commutative and Associative Properties |
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= 24x4 |
Definition of Exponents |
Here is another example: (ab 2)3.
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(ab2)3 = (ab2) · (ab2) · (ab2) |
Definition of exponent 3 |
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= (a · a · a) · (b2 · b2 · b2) |
Commutative and Associative Properties |
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= (a · a · a) · (b · b) · (b · b) · (b · b) |
Definition of exponent 2 |
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= (a · a · a) · (b · b · b · b · b · b) |
Associative Property |
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= a3b6 |
Definition of Exponents |
Another example: (x4y3)2.
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(x4y3)2 = (x4y3) · (x4y3) |
Definition of exponent 2 |
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= (x · x · x · x) · (y · y · y) · (x · x · x · x) · (y · y · y) |
Definition of the exponents 4 and 3 |
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= (x · x · x · x) · (x · x · x · x) · (y · y · y) · (y · y · y) |
Commutative Property of Multiplication |
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= (x · x · x · x · x · x · x · x) · (y · y · y · y · y · y) |
Associative Property of Multiplication |
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= x8y6 |
Definition of Exponents |
Note that these problems are motivating the Properties of Exponents, which are methods for working these problems in a more efficient manner. Some of the Properties of Exponents will be developed later in Session 29.
Evaluate (m2n3)4.
Teacher: "What is 7 times 6?"
Student: "It's 42!"
Teacher: "Very good! - And what is 6 times 7?"
Same student: "It's 24!"
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Date last modified: July 2, 2010.
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By Kris Montis and Timothy Peil
