Download Grade 9 Math - Mrs. M. Brown

Grade 9 Math
1.1 – What is a Power?
Unit 1 – Powers & Exponent Laws
We use exponents to save time when writing out long numbers. For instance, compare writing
2x2x2x2x2x2x2x2x2x2x2x2 to 212 – much easier!
Exponent
224
Base
Power
A power with an exponent of 2 is a square number. A power with an exponent of 3 is a cube number. So, for
example, you would say that 42 is “four squared” and 53 is “five cubed.”
Ex. #1 Write the number of unit squares in the large square as a power.
a.
b.
Answer: It is 5 x 5 which is 52
Answer: It is 5 x 5 x 5 which is 53
Ex. #2 Draw a picture to represent each square number.
a. 2 x 2
b. 32
c. 36
Note – watch for the use of brackets, especially when there are negatives involved! When an exponent is
outside of a pair of brackets, the exponent is applied to everything inside the brackets.
Ex. #3 Write in exponential form.
a.
3 x 3 x 3 x 3 = 34
b.
-2 x -2 x -2 = (-2)3
c.
7 = 71
Ex. #4 Write as a repeated multiplication and in standard form (i.e. evaluate).
a.
23 = (2)(2)(2) = 8
b.
103 = (10)(10)(10) = 1000
c.
-34 = -(3)(3)(3)(3) = -81
d.
(-3)4 = (-3)(-3)(-3)(-3) = 81
e.
–(-3)4 = - (-3)(-3)(-3)(-3) = - 81
How to Use Your Calculator:
Look for the following buttons on your calculator: x2, x3, yx, and/or ^.
Ex. #5 Use your calculator to solve the following.
a.
352 = 1225
b. 63 = 216
c. 87 = 2,097,152
d. 45 = 1024
Ex. #6 a.
32 = (3)(3) = 9
b. –32 = -(3)(3) = -9
c. (-3)2 = (-3)(-3) = 9
3
3
8
2 2
d.    3 
27
3 3
e.
23 8

3 3
f. (0.03)2 = (0.03)(0.03) = 0.0009
When applying exponents to negative bases, notice that exponents that are even will always result in a positive
answer, and exponents that are odd will always result in a negative answer. Be very careful when entering
negative bases in your calculator – always use parentheses or your calculator will misunderstand what you’re
trying to do!
Ex. #7 Solve.
a.
(-3)2 = 9
b.
(-3)3 = -27
c.
(-2)5 = -32
d.
(-2)6 = 64
Assignment
Do #1 – 19 p. 55
Grade 9 Math
Unit 1 – Powers & Exponent Laws
1.1 – What is a Power?
Student Copy
We use exponents to save time when writing out long numbers. For instance, compare writing
2x2x2x2x2x2x2x2x2x2x2x2 to _____ – much easier!
_________________________
______________
224
__________________
A power with an exponent of 2 is a ____________ number. A power with an exponent of 3 is a ____________
number. So, for example, you would say that 42 is “four ___________” and 53 is “five ___________.”
Note – watch for the use of brackets, especially when there are ___________________ involved! When an
exponent is outside of a pair of brackets, the exponent is applied to everything _____________ the brackets.
Ex. #1 Write the number of unit squares in the large square as a power.
a.
b.
Ex. #2 Draw a picture to represent each square number.
a. 2 x 2
b. 32
c. 36
Ex. #3 Write in exponential form.
a. 3 x 3 x 3 x 3 =
b. -2 x -2 x -2 =
c. 7 =
Ex. #4 Write as a repeated multiplication and in standard form (i.e. evaluate).
a. 23 =
b. 103 =
c. -34 =
d. (-3)4 =
e. –(-3)4 =
How to Use Your Calculator:
Look for the following buttons on your calculator: x2, x3, yx, and/or ^.
Ex. #5 Use your calculator to solve the following.
a.
352 =
b. 63 =
c. 87 =
d. 45 =
Ex. #6 a.
32 =
b.
–32 =
c.
(-3)2 =
d.
2
  
3
e.
23

3
3
f.
(0.03)2 =
When applying exponents to ________________ bases, notice that exponents that are ____________ will
always result in a _________________ answer, and exponents that are __________ will always result in a
_____________________ answer. Be very careful when entering negative bases in your calculator – always
use ________________ or your calculator will misunderstand what you’re trying to do!
Ex. #7 Solve.
a. (-3)2 =
b. (-3)3 =
c. (-2)5 =
d. (-2)6 =
Assignment
Do #1 – 19 p. 55