Exponential and Expanded Form
Write 108 in expanded form
10x10x10x10x10x10x10x10
Evaluate 48
65,536
Which number in exponential form tells you how many times to you the other number as a factor?
The exponent
What is 62?
36
What is the square root of 25?
5
EXPLAIN the expanded form of a number as it relates to exponents.
A number times itself as many times as the power given
A student says 43 is 4x3=12. Explain their mistake and give the correct value.
The exponent tells you home many times to use 4 as a factor. Therefore, 43 is 4x4x4=64
Anything to the power of 0 is going to equal...?
1
Which of these is a perfect square?
6, 20, 25, 30, 45, 49
Explain what a square root is
A square root is the number multiplied by itself to get the perfect square
Write 27 in exponential form
33 = 27
TRUE or FALSE:
34 and 92 represent the same value in standard form?
TRUE, both equal 81
A number to the power of 1 is always equal to...?
Itself or the base
Explain which part of the geometrical shape, the square, does the perfect square represent? And which part does the base represent?
1. The area in square units
2. The length and width
NO CALCULATOR:
If you put the square root of 145 in the calculator what will your answer most likely look like?
It will be a decimal because 145 is not a perfect square
Give the exponential and expanded form of the number 32
25
2x2x2x2x2
Explain 3 ways you could say 53?
5 to the power of 3
5 to the third power
5 cubed
Which button on the calculator do you use to evaluate any number in exponential form?
ab
A square has an area of 121 square units. What is the length of one side?
11 units because 11x11 is 121
A square garden has an area of 196 square feet. If fencing is needed around all four sides, how many feet of fencing are required? (What is the perimeter?)
56 ft
The sqrt of 196 = 14 and each side is equal so the perimeter is 14+14+14+14 or 14x4 which equals 56
Explain why 53 is not 15
And give the correct standard form of 53
Because exponents tell you how many times you multiply the base by itself not multiplication of the base and the exponent. So 53 would be 125
Billy is helping a classmate understand how to simplify exponents. They are solving the problem below.
82
Which statement would be correct for Billy to use in explaining exponents to his classmate?
A The base 8 and exponent 2 means to multiply 2x2x2x2x2x2x2x2.
B The base 8 and exponent 2 means to multiply 2x8.
C The base 8 and exponent 2 means to add 8+8.
D The base 8 and exponent 2 means to multiply 8x8.
D.
Explain why one may need to write a number in exponential form?
To avoid writing out a huge long number
Name all of the perfect square between 1 and 100 that are also multiples of 4.
4, 16, 36, 64, 100
The square root find the base being square to get the perfect square and the perfect square is what is being square rooted to find the base or the L&W of a square.