Exponents and Order of Operations

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Exponents and Order of Operations
Section 1.7
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An exponent is a shorthand notation for repeated
multiplication.
3 3 3 3 3
3 is a factor 5 times Using
an exponent, this product can be written as
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This is called exponential notation. The
exponent, 5, indicates how many times the base,
3, is a factor.
Read as three to the fifth power or the fifth
power of three.
3 3 3 3 3
3 is a factor 5 times
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Reading Exponential Notation
4
is read as four to the first power.
4 ? 4
is read as four to the second power or four
squared.
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Reading Exponential Notation . . .
4 ? 4 ? 4
is read as four to the third power or four
cubed.
4 ? 4 ? 4 ? 4
is read as four to the fourth power.
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Usually, an exponent of 1 is not written, so when
no exponent appears, we assume that the exponent
is 1. For example,
2 21 and 7 71.
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To evaluate an exponential expression, we write
the expression as a product and then find the
value of the product.
35 3 3 3 3 3 243
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An exponent applies only to its base. For example,
4 23 means 4 2 2 2.
Dont forget that 24 is not 2 4. 24
means repeated multiplication of the same factor.
24 2 2 2 2 16, whereas 2 4 8
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Order of Operations
1. Perform all operations within grouping symbols
such as parentheses or brackets. 2. Evaluate any
expressions with exponents. 3. Multiply or divide
in order from left to right. 4. Add or subtract
in order from left to right.
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