Definition of Let b be a nonzero real number. Then, Definitions of and Definition of Let b be a nonzero real number. Then, Definition of Let n be an integer and b be a nonzero real number. Then,

Patterns As the exponents decrease by 1, the resulting expressions are divided by 3 3³ = 27 3² = 9 3¹ = 3 3° = 1 For the pattern to continue, we define 3° = 1

Simplifying Expressions with a Zero Exponent By Definition By Definition 4° = 1 (-4)° = 1 -4° = -1 The exponent 0 applies only to 4 z° = 1 By Definition -4z° = -4∙z° = -4∙1 = -4 The exponent 0 applies only to z. The parentheses indicate that the exponent, 0, applies to both factors 4 and z (4z)° = 1

3³ = 27 3² = 9 3¹ = 3 3° = 1 Definition of As the exponents decrease by 1, the resulting expressions are divided by 3 When the exponent is negative take the reciprocal of the base and change the sign of the exponent

By Definition By Definition Simplify The base if -3 and must be enclosed in parentheses. (-3)(-3)(-3)(-3) = 81 Take the reciprocal of the base, and change the sign of the exponent. Simplify Take the reciprocal of the base, and change the sign of the exponent. Simplify Apply the power of a quotient rule. Take the reciprocal of the base, and change the sign of the exponent. Apply the exponent of 3 to each factor within parentheses. Simplify Note that the exponent, -3, applies only to x.

Class fun

SCIENTIFIC NOTATION 2 4 0,0 0 0,0 0 0,0 0 0,0 0 0 x 1014 2.4 x 1014 Scientific notation takes a number (particularly a large one with lots of zeros or a small one with lots of zeros between the decimal point and other digits) and uses powers of 10 to express it more easily. 2 4 0,0 0 0,0 0 0,0 0 0,0 0 0 x 1014 1 2 3 4 5 6 7 8 9 10 11 12 13 14 The decimal should be after the first nonzero digit. To keep the number equal we’d need to multiply by a power of 10. Count how many decimal places to get to original decimal point to see what that power of 10 should be. 2.4 x 1014

If the number was very small we'd do the same thing, but since we'd be counting in the opposite direction, our power of 10 would be negative. 0 . 0 0 0 0 0 0 3 6 x 10 -7 7 6 5 4 3 2 1 The decimal should be after the first nonzero digit. To keep the number equal we’d need to multiply by a negative power of 10. Count how many decimal places to get to original decimal point to see what that power of 10 should be. 3.6 x 10 -7