Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
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Rules of Exponents – Notes – Textbook Section 5.08 Powers: an expression that represents Ex. 1: 52 = Base: a number that is used as a Exponent: multiplication. Ex. 3: 5²: Ex. 2: 4³ = in the repeated multiplication. the base is used as a factor in repeated is the base; factors of is the exponent; in other words, there are . Special Note: Any number raised to the 0th power (with an exponent = 0) equals ______ Ex. 4: 50 = __________ ! !
!
= __________ (𝑥𝑦 ! )! = ___________ Special Note: Any number raised to the 1st power (exponent = 1) equals Ex. 5: x1 = _________ ! !
!
= __________ (38.2321)¹ = _____________ PRODUCTS OF POWERS Product -­‐ __________________________________________________________________. Product of Powers Property: Let a be a real number, and let m and n be positive integers. 𝑎! ∗ 𝑎! = 𝑎!!! To multiply powers having the same base, _______________ the exponents. Ex. 6: 5! (5! ) = _______________________________ = _______________________ Ex. 7: 7! ∗ 7! = _____________________________ = ______________________ 1
Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Ex. 8: 𝑥 ! ∗ 𝑥 ! = _____________________________ = _____________________ Ex. 9: !
! !
!
!
= _____________________________ = ____________________ POWERS OF POWERS Powers of Powers Property: Let a be a real number, and let m and n be positive integers. 𝑎! ! = 𝑎!∗! To find a power of a power, _________________________ the exponents. Example 10: (52)3 = _________________________________ = _________________ Example 11: (7³)5 = _________________________________ = ________________ Example 12: (1228)1 = _________________________________________ = _______________ !
Example 13: !
² 6 = _________________________________________ = _______________ Example 14: Determine which of the following expressions are equal to 2!" . Show work to justify your answer. Expression Equal to 𝟐𝟏𝟐 Justification 2!" + 2! 2
!
!!
2
2
!
!
2 !!
+ 2 2! 2! 2
Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
You Try: Simplify the expression. Show your work. Write your answer using exponents. 1. 5! ! 3. 10! ! 5. 4! ∗ 4! 2. 61 *64 4. 6! ! 6. (4! )! 7. Determine which of the following expressions are equal to 2!" . Show work to justify your answer. Expression Equal to 𝟐𝟏𝟐 Justification 4 2!" !
!
!
!
2 ∗ 2 2 + 2 2!" 2! 3