Name: _______________________________________ Algebra 1: Exponents and Polynomials
Topic E1: Multiplication with Exponents & Scientific Notation | VERSION B Name the base and exponent in the following expressions. Then, use the definition of exponents as repeated multiplication to simplify. 1.
5.
! !
!
The base is 8! The exponent is The base is The exponent is ! !
!
= 8! = 2.
6.
−12 ! −
! !
!
The base is The base is The exponent is The exponent is −12 ! = 3.
−
! !
!
= −10 ! The base is Use the properties of exponents to simplify the following expressions: The exponent is −10
4.
!
= 7.
𝑣 ! ⋅ 𝑣 ! = 8.
𝑦 ! ⋅ 𝑦 ! ⋅ 𝑦 !! ⋅ 𝑦 !" = 9.
𝑏 !
−2 ! The base is The exponent is −2
!
!
= = www.varsitylearning.com 1 Name: _______________________________________ Algebra 1: Exponents and Polynomials
Topic E1: Multiplication with Exponents & Scientific Notation | VERSION B Use the properties of exponents to simplify the expressions. You may leave your answer as a number to a power. !
10. −6𝑢
16. Write 87,500 in scientific notation: = 17. Write 7.06×10! in standard form: !
11. −3𝑎𝑏
12. 4𝑝 !
!
13. 𝑡 !
𝑡!
!
= 18. Find the volume of a cube if each side is 38 inches long? Round to the nearest tenth. The volume is in³. = !
= 19. Find the volume of a cube if each side is 21 inches long? The volume is in³. 14. 2𝑟 !
15.
!
4 ! !
𝑦 𝑝
5
2𝑟
!
!
= = 20. If a person is 33 years old, they will have been alive for more than 1,040,000,000 seconds. Write this last number in scientific notation. www.varsitylearning.com 2 Name: _______________________________________ Algebra 1: Exponents and Polynomials
Topic E1: Multiplication with Exponents & Scientific Notation | VERSION B Name the base and exponent in the following expressions. Then, use the definition of exponents as repeated multiplication to simplify. 1.
5.
!
The base is !
The exponent is 2 The exponent is 2 8! = 8 8 = 64 −12 ! The base is −12 6.
! !
!
−
= ! !
!
!
!
!
!
=
!
!"
3
4
The exponent is 2 The base is − −12 ! = −12 −12 = 144 The exponent is 2 −
3.
!
8! The base is 8 2.
! !
! !
!
= !
!"
−10 ! The base is −10 The exponent is 2 −10
4.
!
= −10 −10 = 100 −2 ! Use the properties of exponents to simplify the following expressions: 7.
𝑣 ! ⋅ 𝑣 ! = 𝑣 !!! = 𝑣 ! 8.
𝑦 ! ⋅ 𝑦 ! ⋅ 𝑦 !! ⋅ 𝑦 !" = 𝑦 !!!!!!!!" = 𝑦 !" 9.
𝑏 !
The base is −2 The exponent is 3 −2
!
= −2 −2 −2 = −8 !
= 𝑏 !⋅! = 𝑏 ! www.varsitylearning.com 3 Name: _______________________________________ Algebra 1: Exponents and Polynomials
Topic E1: Multiplication with Exponents & Scientific Notation | VERSION B Use the properties of exponents to simplify the expressions. You may leave your answer as a number to a power. !
10. −6𝑢
= −6
!
16. Write 87,500 in scientific notation: 8.75×10! 𝑢 ! = −6! 𝑢 ! or − 216𝑢 ! 17. Write 7.06×10! in standard form: 706,000 !
11. −3𝑎𝑏
12. 4𝑝 !
!
13. 𝑡 !
𝑡!
!
= −3
!
= 4
!
!
!
𝑎
⋅ 𝑝!
!
𝑏 ! = −27𝑎 ! 𝑏 ! = 1024 ⋅ 𝑝 !⋅! = 1024𝑝 !" 18. Find the volume of a cube if each side is 38 inches long? Round to the nearest tenth. The volume is 54872 in³. = 𝑡 !⋅! 𝑡 !⋅! = 𝑡 !" 𝑡 !" 19. Find the volume of a cube if each side is 21 inches long? The volume is 9261 in³. = 𝑡 !"!!" = 𝑡 !" 14. 2𝑟 !
!
2𝑟
!
= 2! 𝑟 !⋅! 2! 𝑟 ! = 128𝑟 !" 512𝑟 ! = 128 ⋅ 512 𝑟 !"!! = 65,536𝑟 !" 15.
4 ! !
𝑦 𝑝
5
!
= 4
5
!
𝑦 !⋅! 𝑝 !⋅! =
256 !" !"
𝑦 𝑝 625
20. If a person is 33 years old, they will have been alive for more than 1,040,000,000 seconds. Write this last number in scientific notation. 1.04×10! www.varsitylearning.com 4