Download Math 9 Study Guide Unit 2 Unit 2 Powers and Exponents A POWER

Math 9
Study Guide
Unit 2 Powers and Exponents
A POWER is the integer and the exponent.
Power: 35 (where 3 is the base and 5 is the exponent)
A power written as repeated multiplication:
35 = 3x3x3x3x3
A power written in standard form (the answer):
35 = 243
A square number is the integer base with the exponent of 2:
32
A cube number is the integer base with the exponent of 3:
33
Working with Negatives
-34 = -1(3x3x3x3) = -81
(-34) = -3x3x3x3 = -81
-(-34) = -3x3x3x3 (do what is in the brackets first)
-(-34) = -1(-81) = 81
(-3)4 = (-3)(-3)(-3)(-3)
(-3)4 = 81
Zero Exponent
A power with an integer base, other than 0, and an exponent of 0 is always 1.
20 = 1
130 = 1
(-5)0 = 1
BUT…
-40 = -1
Unit 2
Math 9
Study Guide
Powers of Ten
Use the place value chart.
Ex.
thousands
3
hundreds
4
tens
5
ones
2
3452 = 3000 + 400 + 50 + 2
= (3x1000) + (4x100) + (5x10) + (2x1)
= (3x103) + (4x102) + (5x101) + (2x100)
Quotient – answer to a division equation
Product – answer to a multiplication equation
Simplify – work as far as the last power
Evaluate – find the final answer
Exponent Laws
Product of a Power
If the bases are the same, add the exponents.
Ex. 23 x 22 = 23+2 = 25
(2)(2)(2) x (2)(2) = 25
Quotient of a Power
If the bases are the same, subtract the exponents.
Ex. 74 ÷ 73 = 7x7x7x7 = 74-3 = 71
7x7x7
Power of a Power
A power is being raised to another power.
Ex. (32)4 = 32x4 = 38
Power of a Product
The base of the power may be a product.
Ex. (3 x 4)5 = 35 x 45
Power of a Quotient
The base of the power may be a quotient.
Ex. (5/6)3 = 53
63
Unit 2