Exponents
What does 23 equal?
23 = 2 x 2 x 2 = 8
Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 4 cups of rice, how many cups of water does she need?
2(4) = 8
8 cups of water.
Evaluate the following expression:
4x + 6x when x = 3
30
What is the prime factorization of 24?
24(3 x 2 x 2 x 2)
Solve for x: x - 4 = 9
What is the expansion of 46?
4 x 4 x 4 x 4 x 4 x 4
Jackson ran 4 miles on Monday, 12 miles on Tuesday, 1 mile on Wednesday, 8 miles on Thursday, and 5 miles on Friday. What was the total number of miles Jackson ran?
4 + 12 + 1 + 8 + 5 = 40 miles total
What does each letter in P.E.M.D.A.S. stand for ? Why do we use P.E.M.D.A.S.?
P:
E:
M & D:
A & S:
P: ( ) parenthesis
E: 22 Exponents
M & D: Multiplication and Division
A & S: Addition and Subtraction
We use PEMDAS as rules for solving algebra problems.
What does prime factorization mean?
Prime Factorization means taking a number apart into its smallest prime factors.
8 = 4 x 2 = 2 x 2 x 2
Solve for x: x + 5 - 2 = 11
x = 8
What is the exponent form of:
5 x 5 x 5 x 5 x 5 x 5 x 5
57
Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.
R = c + 3
Is the following expression 20h - 5 = 15h + 35 true when h = 6?
No
115 does not equal 125
What is the highest prime factor less than 100?
97
Simplify:
2x2 + 3x + 5 + 4x2 + 5x + 6
6x2 + 8x + 11
Simplify:
52 - 23
52 = 25
23 = 8
25 - 8 = 17
Rita bought a sofa that was on sale for $1299. She paid a total of $1409, including sales tax. Find the amount of the sales tax, t, by solving the equation 1299 + t = 1409.
t = $110
Is the following an expression or an equation? Why?
6x + 5y - 3z
Expression b/c there is no equal sign
What is the LCM of 16 and 24?
16(2 x 2 x 2 x 2)
24(2 x 2 x 2 x 3)
LCM (2 x 2 x 2 x 2 x 3) = 64
Solve for w: 19 less than w is 56
w = 75
Write in exponent form and simplify:
(4 x 4 x 4 x 4) - (5 x 5 x 5) - (2 x 2 x 2 x 2 x 2)
(44) - (53) - (25)
256 - 125 - 32
99
Paper plates are sold in packages of 12 and party cups come in packs of 8. What is the smallest number of plates and cups you can purchase if you want to have the same number of each? (Hint: it is the LCM!)
24
Translate the following into math:
Seven times the difference of y and 1
7(y - 1)
Explain the process of finding the LCM of two numbers using prime factorization
Step 1: Find the prime factorization of both numbers
8(2 x 2 x 2) 12(3 x 2 x 2)
Step 2 Stack like terms on top of each other and non-like terms by themselves
8(2 x 2 x 2)
12(2 x 2 x 3)
LCM(2 x 2 x 2 x 3)
Step 3: Multiply the non-like terms to find the LCM
LCM(2 x 2 x 2 x 3) = 24
72 - (2 + 8 · 4)
15