Powers and Scientific Notation
Identify for the following the base and the exponent.
84
8 - base
4 - power/exponent
Define the following: like terms
Any 2 or more terms that contain the same variable with the same exponent
a0= 1 is an example of which exponent law?
Zero exponent rule -- any number to the power of 0 equals 1.
Which of the following does not belong?
x3 3x2 4x3 2x3
3x2
Expand the following expression:
= 3x(x3 - 5)
= 3x4 - 15x
What’s the difference between? Explain why.
-32 vs (-3)2
-32 = -9
(-3)2 = 9
The brackets imply that the negative is attached to the base, therefore when multiplied twice it becomes positive. No brackets means the negative still applies after the power/exponent has been applied.
Define the following: variable
Is a letter that represents an unknown value.
When multiplication is the operation in the expression given, what is the exponent rule?
ie. (z4)(z3)= ?
The produce rule: add the exponents when you multiply
Which of the following does not belong?
-y xy 2y -3y
Expand the following:
= (10x3 + 2x)(4)
= 40x3 + 8x
Any number to the power of 1 ie. 51 will equal...
Example: 5
What is a constant?
Constant is a number, there are no variables attached.
(2xy4)2 is an example of which exponent rule?
How many terms are in the following expression? What are they?
3x2 - 5y + 10x - 25 - 3y
4: x2, y, x, 25 (constant)
Expand the following:
= -w(2x - 5w2)
= -2xw + 5w3
The following number is in scientific notation, what is its value?
2.58 X 104
25 800
What does to the power of mean?
Power tells us the exponent, how many times the base is multiplied.
When dividing, what is the rule for exponents?
ie. 56/53 = ?
Quotient Rule: the exponents are subtracted.
Simplify the following expression:
3 - 11y - 8 - y = ?
= -5 - 12y
Expand and simplify the following:
= -2y(x + 3) + 5(y-5)
= -2xy - 6y + 5y - 25
= -2xy -y -25
The following number is in scientific notation, what is its value?
1.6 X 10-3
0.0016
What is the difference between expanded and simplified form?
Expanded form: the base is written out as many times as the exponent tells us ie. y4= (y)(y)(y)(y)
Simplified form: is the base with the exponent ie. x8
How do I make a negative exponent positive?
ie. 9-7
You flip the fraction and the exponent becomes positive.
ie. 1/97
Simplify the expression and substitute in
x=2 and y = 5
-8x + 3y - (-3x) + y =
= -8x + 3x + 3y + y
= -5x + 4y
= (-5)(2) + 4(5)
= -10 + 20
= -10
Expand and simplify the following:
= 3m(m2 - 5) - (2m2 - m)
= 3m3 - 15m - 2m2 + m
= 3m3 -14m - 2m2