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ACC Module #2 Unit 2.3

ACC Module #2 Unit 2.3

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ACC Module #2 Unit 2.3

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  1. DemingEarly College High SchoolUnit 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.3 Exponents

  2. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents Exponents are used in mathematics to express a number or variable multiplied by itself a certain number of times. For example, means x is multiplied by itself three times or x * x * x. In this expression x is called the base and 3 is the exponent. Exponents can be used in more complex problems when they contain fractions and negative numbers.

  3. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents Fractional Exponents can be explained by looking first at the inverse of exponents, which are roots. Given the expression , the square root can be taken, , cancelling out the 2 and leaving x by itself, if x is positive. Cancellation occurs because can be written with exponents, instead of roots, as . The numerator of 1 is the exponent, and the denominator of 2 is called the root (which is why it is referred to as a square root). Taking the square root of is the same as raising it to the ½ power.

  4. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents Written out in mathematical form, it takes the following progression: . From properties of exponents, 2 * ½ = 1 is the actual exponent of x. Another example can be seen with . The variable x, raised to four-sevenths, is equal to the seventh root of x raised to the fourth power: . In general, and

  5. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents and Simplify:

  6. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents and Simplify:

  7. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents Negative exponents also involve fractions. Whereas can also be written as can be rewritten as . A negative exponent means the exponential expression must be moved to the opposite spot in a fraction to make the exponent positive. If the negative appears in the numerator, it moves to the denominator. If the negative appears in the denominator, it is moved to the numerator.In general, and and are reciprocals.

  8. Unit 2.0 QAS 2.3 Exponents 2.3.1 Properties of Exponents Take, for example, the following expression: . Since a is raised to the negative fourth power, it can be moved to the denominator. Since c is raised the negative fifth power, it can be moved to the numerator. The b variable is raised to the positive second power, so it does not move.This is the simplified expression is: Remember, PEMDAS states that exponents are calculated after any parenthesis and grouping symbols, but before any multiplication, division, addition, and subtraction.

  9. Unit 2.0 QAS 2.3 Exponents 2.3.2 The Evaluation of Positive Real Roots and Exponents There, are a few rules for working with exponents. For any numbers a, b, m, n, the following hold true: Any number including a fraction, can be an exponent. The same rules apply.

  10. Unit 2.0 QAS 2.3 Exponents 2.3.2 The Evaluation of Positive Real Roots and Exponents Simplify the following expressions: ? = ?

  11. Unit 2.0 QAS 2.3 Exponents 2.3.2 The Evaluation of Positive Real Roots and Exponents Simplify the following expressions: ? = ?

  12. Unit 2.0 QAS 2.3 Exponents 2.3.2 The Evaluation of Positive Real Roots and Exponents Simplify the following expressions: = ? = ?

  13. Unit 2.0 QAS 2.3 Exponents 2.3.2 The Evaluation of Positive Real Roots and Exponents Simplify the following expressions: = ? = ?

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