Lesson 601 After completing this lesson you will be able to say I can write numerical expressions involving wholenumber exponents I can evaluate numerical expressions involving wholenumber exponents ID: 534272
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Slide1
Numerical Expressions
Lesson
6.01Slide2
After completing this lesson, you will be able to say:
I
can
write numerical expressions involving whole-number exponents
.
I
can
evaluate numerical expressions involving whole-number exponents
.
I
can
solve order of operation expressions that contain exponents.Slide3
Key Terms
Exponential form:
A
number including a base and an exponent
.
Base:
The
number that is multiplied by itself when written
in
exponential form
.
Exponent:
A
number that is written above and to the right of a
base
to indicate how many times to multiply the
base
by itself; sometimes called a powerSlide4
Exponential form
Exponential form is just a simplified way of writing a multiplication expression where a number is being multiplied by itselfSlide5
Writing a Number in Exponential formSlide6
Area in Exponential Form
Since the 5 is being multiplied by itself 2 times, you can use an exponent of 2. The area 5
ft
× 5
ft
written in exponential form is 5
2
ft
2
.
When the exponent is a 2, this is called squaring the base. So you can say
"five squared."Slide7
Volume in Exponential Form
To calculate the volume of the circus cube you would multiply 5
ft
× 5
ft
× 5 ft.
5 is the base, but this time it is multiplied 3 times so the exponent in this case is 3. Therefore, the exponential form of the volume is 5
3
ft
3
.
When an exponent is a 3, this is called cubing the base. So you can say
"five cubed."Slide8
Example using Exponential Form
The goal of this new circus act is for the performers to knock over as many pins as possible. Each pin will knock over three other pins, and each of those will knock over three more pins, and so on.
There are
five total rows
of pins. The expression to see how many pins to knock down in the fifth row is created by
multiplying 3 five times
. You can write this expression as
3 × 3 × 3 × 3 × 3
or in exponential form as 3
5Slide9
Try it
Ginger, the circus mouse, gave birth to twins. Each of the twins then gave birth to twins. Then those twins gave birth to twins.Slide10
Check your work
To understand how the mice population grew, you would multiply 2 three times
.
So 2 × 2 × 2 =
2
3
or "two cubed."Slide11
Reading Exponents
An exponent is sometimes referred to as a power. So 5
2
can be read as "five to the power of two."
Here are a few other variations for reading exponential expressions:
5
2
5
3
5
4
5 to the second power
5 to the third power
5 to the fourth
power
5 to the power of 2
5 to the power of 3
5 to the power of 4
5 squared
5 cubed
5 raised to the second power
5 raised to the third power
5 raised to the fourth power
5 with an exponent of 2
5 with an exponent of 3
5 with an exponent of 4Slide12
Typing Exponents
Typing Exponents
An easy way to represent an exponent is to use the ^
symbol (above the number 6 on your keyboard).
So
, 5
3
can be typed as 5^3.Example: 64 = 6^4Slide13
Simplifying exponential numbers
3
5
= 3 x 3 x 3 x 3 x 3 =
3 x 3 x 3 x 3 x 3
9 x 3 x 3 x 3
27 x 3 x 3
81 x 3
243
When simplifying an exponent, you must remember that
7
3
= 7 × 7 × 7. It does not equal 7 × 3 or
7
·
3
or 73
CautionSlide14
Try it
Simplify the exponential expression of 6.2
4
. Be sure to round your answer to the nearest tenths placeSlide15
Check your work
6.2
4
= 6.2 × 6.2 × 6.2 × 6.2 = 1,477.6336
This is 1,477.6 when rounded to the tenths placeSlide16
Evaluating Numerical Expressions
When simplifying an expression, you must always follow the order of operations.
Order of operations
:
The rules of which calculation comes first when evaluating an expressionSlide17
Simplifying and Expression
Steps to
Simplify an expression
Step 1:
simplify inside parenthesis
Step 2
: simplify
the
exponents
Step
3
:
evaluate any multiplication and/or division from
left
to
right
Step 4
: complete any addition and/or subtraction from
left
to rightSlide18
ExampleSlide19
Try it
Simplify the expression
4
3
÷ (7 − 3) ×
2Slide20
Check your work
4
3
÷
(7 − 3)
×
2
43 ÷ 4 × 264 ÷ 4
×
2
16 x 2
32Slide21
Now that you completed this lesson, you should be able to say:
I
can
write numerical expressions involving whole-number exponents.
I
can
evaluate numerical expressions involving whole-number exponents.
I
can
solve order of operation expressions that contain exponents.