Grade 7 Math: 1.5
Chap.1 Factors and Exponents – Lesson #3
P. 16-17 Powers
*Would you rather take $100 000 cash OR take one dollar the first day and triple it everyday
for 11 days days? (Re-visit at end of class)
Power: a numerical __numerical expression_____ that shows __repeated_____ multiplication.
(also known as a number written in exponential form
Eg. 5 x 5 x 5 x 5 = 54
Exponent
Base
Base: the _factor_____ you multiply.
Exponent: the number of factors you multiply. (the number of times you repeat the base as a
factor)
Practice: Write each repeated multiplication as a power.
a) 3 x 3 = ____32_
b) 9 x 9 x 9 = __93
Write the following power as repeated multiplication: 63 = __6 x 6 x 6_____
Standard Form: the solution to a power. Eg : 63 = _216____
Naming powers: 45 is a power, which includes a base and an exponent, and can be named:
four to the fifth power
four to the exponent five
the fifth power of four.
45 can be written as repeated multiplication: 4 x 4 x 4 x 4 x 4 and then evaluated or solved and
written in standard form: 1024.
Try this: Write 74 in words, in three ways: _Seven to the fourth, seven to the exponent four and
the fourth power of seven.
Square Number: the ____product________ of ___two_______ equal factors.
Eg. 16 is the square of 4, since 4 x 4 = 16 or 42 = 16
42 is read as four squared.
Area of a square: A = s2
Cubic Number: the ___product______ of __three___________ equal factors.
Eg. 8 is the cube of 2, since 2 x 2 x 2 = 8 or 23 = 8
23 is read as two cubed.
Volume of a cube: V = s3
Grade 7 Math: 1.5
Writing a number as a power of a given base factor:
If you are given a number and then are asked to write it as a power of another number:
Eg. Write 243 as a power of 3 (243 is the solution to the power, the base must be 3, raised to
some exponent value which must be calculated)
1. Use repeated division method:
1
3 3
Divide 3 into 243, write the answer above 243, then divide 3 into 81,
3 9
write the answer above 81, then divide 3 into 27 ….. until the answer
3 27
becomes 1. The number of 3’s used as the divisor becomes the
3 81
exponent to be placed on the base of 3.
3 243
So 243 written as a power of 3: 243 = 35
2. Use repeated multiplication method:
243 = 3 x 3 x 3 x 3 x 3
= 9x3x3x3
Multiply the base factor “3” by itself as many times as needed
to arrive at the product of 243.
= 27 x 3 x 3
= 81 x 3
= 243
Try This: Write 256 as a power of 4: 44
*Would you rather take $100 000 cash OR take one dollar the first day and triple it everyday
for 11 days? (Re-visit at end of class)
Day
Repeated
Power
Prize ($)
Multiplication
1
3
31
3
2
2
3x3
3
9
3
3
3x3x3
3
27
4
4
3x3x3x3
3
81
5
5
3x3x3x3x3
3
243
6
3x3x3x3x3x3
36
729
7
7
3x3x3x3x3x3x3
3
2187
8
8
3x3x3x3x3x3x3x3
3
6561
9
9
3x3x3x3x3x3x3x3x3
3
19683
10
3x3x3x3x3x3x3x3x3x3
310
59049
11
11
3x3x3x3x3x3x3x3x3x3x3 3
177147
Grade 7 Math: 1.5
Assignment: P.18-19 # 5, 6, 7 AD, 9 DEF, 12, 13, 17, 19 Bonus #20
Due: __________________