Download Algebra 2: Real Numbers and Algebraic Expressions

Algebra 2: Real Numbers and Algebraic Expressions
Name: ___________________________________________ Topic A4: Exponents and Scientific Notation | VERSION B 1.
The following is a list of steps for the order of operations. Write the correct step number in the blanks. Write the following with positive exponents. Then simplify as much as possible. 7.
3!! = 8.
______ Simplify all numbers with exponents, working from left to right if more than one of these expressions is present. ______ Perform all additions and subtractions left to right. ______ Work all multiplications and divisions left to right. 3
2
!!
= ______ Begin with the expressions in the innermost parentheses or brackets and work your way out. Use the properties of exponents to simplify the following as much as possible. 2.
6! = Multiply. 9.
3.
8
9
!
8𝑎 ! ⋅ 3𝑏 ! = = 10. −5𝑎 ! 𝑐 ! ⋅ 5𝑏 ! 𝑐 = 2
7
!
4.
−
= 5.
𝑥 ! ⋅ 𝑥 ! = Divide. (Assume all variables are nonzero.) 11. 6.
−4𝑥 ! 6𝑥 ! = !"! ! ! !
!!! ! ! !
= www.varsitylearning.com 1 Algebra 2: Real Numbers and Algebraic Expressions
Name: ___________________________________________ Topic A4: Exponents and Scientific Notation | VERSION B Use properties of exponents to simplify the expression. Write all answers with positive exponents only. (Assume all variables are nonzero.) 12. ! !!
!!
Write the following numbers in scientific notation. 16. 39,300 = = 17. 0.656 = Write the following number in expanded form. 13. !
!!
!!
18. 6.77×10! = = 19. 6.37×10!! = 14. !! ! ! !
!! ! ! !!
= Use the properties of exponents to simplify the following expression. Write the answer in scientific notation. 20. 15. ! !! !! !
! !! ! ! ! !
!×!"! !×!"!!
!×!"!
= !
= www.varsitylearning.com 2 Algebra 2: Real Numbers and Algebraic Expressions
Name: ___________________________________________ Topic A4: Exponents and Scientific Notation | VERSION B 1.
The following is a list of steps for the order of operations. Write the correct step number in the blanks. Write the following with positive exponents. Then simplify as much as possible. !
7.
3!! = 8.
!
2 Simplify all numbers with exponents, working from left to right if more than one of these expressions is present. 4 Perform all additions and subtractions left to right. 3 Work all multiplications and divisions left to right. 1 Begin with the expressions in the innermost parentheses or brackets and work your way out. 3
2
!!
!
= !
Use the properties of exponents to simplify the following as much as possible. 2.
6! = 36 Multiply. 9.
8
9
!
= !"
3.
4.
2
−
7
5.
𝑥 ! ⋅ 𝑥 ! = 𝑥 ! !
!"
= 8𝑎 ! ⋅ 3𝑏 ! = 24𝑎 ! 𝑏 ! !
!"
10. −5𝑎 ! 𝑐 ! ⋅ 5𝑏 ! 𝑐 = −25𝑎 ! 𝑏 ! 𝑐 ! Divide. (Assume all variables are nonzero.) 11. 6.
−4𝑥 ! 6𝑥 ! = −24𝑥 ! !"! ! ! !
!!! ! ! !
= 3𝑎! 𝑏 ! www.varsitylearning.com 3 Algebra 2: Real Numbers and Algebraic Expressions
Name: ___________________________________________ Topic A4: Exponents and Scientific Notation | VERSION B Use properties of exponents to simplify the expression. Write all answers with positive exponents only. (Assume all variables are nonzero.) 12. ! !!
!!
= !
! !!
Write the following numbers in scientific notation. 16. 39,300 = 3.93×10! 17. 0.656 = 6.56×10!! 13. !
!!
!!
Write the following number in expanded form. 18. 6.77×10! = 67,700 = 𝑥16 19. 6.37×10!! = 0.000637 14. !! ! ! !
=
!! ! ! !!
!! !!
!
Use the properties of exponents to simplify the following expression. Write the answer in scientific notation. 20. !×!"! !×!"!!
!×!"!
= 1.875×10!!" 15. ! !! !! !
! !! ! ! ! !
!
= 1 www.varsitylearning.com 4