Laws of Exponents Print Activity
Name: __________________
Laws of Exponents Print Activity
1. Use the Product Law in the “Explore It” mode for the following exercise.
Move the slider bars as directed:
• m (purple) to 2
• n (orange) to 3
• x (red) to 4
a. Use the above example in the “Explore It” mode to complete the following:
[pic] Exponential form Expanded form
[pic] [pic]
b. Complete all the missing parts in the following table:
|xm [pic]xn |Exponential form |Expanded form |
| | | |
|Eg. 31 [pic]34 |(3)1+4 = (3)5 |(3) [pic](3)(3)(3)(3) |
| | | |
|52 [pic]5 |(5)2+3 = ______ | |
| | | |
|(-4) [pic](__) |(___) + = ______ |(-4)(-4) [pic](-4)(-4) |
|Eg. (3)-2 [pic](3)4 | |[pic] |
| |(3)-2+4 = (3)2 | |
| | | |
|(-2)-1 [pic](__)-3 |(-2) + = ______ | |
| | | |
|(___) ×(___) |(-6)3+2 [pic]= ______ | |
| | | |
|(2)4 [pic](2)-3 |(2) + = ______ | |
c. Complete the Product Law:
When multiplying like bases you must _________ the exponents.
2. Use the Quotient Law in the “Explore It” mode for the following exercise.
Move the slider bars as directed:
• m (purple) to 5
• n (orange) to 3
• x (red) to 4
a. Answer the following using the above example in the “Explore It” mode:
[pic] Exponential form Expanded form
[pic] [pic]
b. Complete all the missing parts in the following table:
|xm [pic]xn |Exponential form |Expanded form |
|Eg. | | |
|34 [pic]31 |[pic] |[pic] |
| |[pic] | |
| | | |
|53[pic]5 |[pic] | |
| | | |
|(-3)3[pic](-3)2 |[pic] [pic] = ____ | |
| | | |
|(-4) [pic] (___) |(___) [pic] = _____ |[pic] |
|Eg. (3)-4 [pic](3)2 | |[pic] |
| |[pic] | |
| | | |
|(-2)-1 [pic] (__)-3 |(-2) [pic] = ____ | |
| | | |
|(__)-3 [pic](__)2 |(-6)-3-2 = _____ | |
| | | |
|(2)3 [pic] (2)-3 |(-2) [pic] = ____ | |
c. Complete the Quotient Law:
When dividing like bases you must ______the exponents.
3. Use the Power of a Power Law in the “Explore It” mode for the following exercise.
Move the slider bars as directed:
• m (purple) to 2
• n (orange) to 3
• x (red) to 4
a. Use the above example in the “Explore It” mode to complete the following:
[pic] Exponential form Expanded form
[pic] [pic]
[pic] (__) ×(__) ×(__)
(__) ________________
____ ____________
b. Complete all the missing parts of the following table:
|(xm )n |Exponential form |Expanded form |
|e.g. (23 )2 |[pic] |(2)(2)(2)(2)(2)(2) |
| | | |
|(52) |[pic] |____________________ |
| | | |
|((-3)3)2 |(-3) [pic] = _____ |____________________ |
| | | |
|((-4) ) 2 |(-4) [pic] = _____ |(-4)(-4)(-4)(-4) |
|e.g.(-3)-4)2 | | |
| |[pic] |[pic] |
| | | |
|((4)-3 )-2 |(4) [pic] = _____ |_________________________ |
| | | |
|((-2)-1 )-3 |(___) [pic] = _____ |_________________________ |
| | | |
|((3)2 ) -2 |(___) [pic] = _____ |_________________________ |
c. Complete the Power of a Power Law:
When raising a power to another power you must ______ the exponents.
4. Use the Power of a Product Law in the “Explore It” mode for the following exercise.
Move the slider bars as directed:
• m (purple) to 2
• y (green) to 3
• x (red) to 4
a. Use the above example in the “Explore It” mode to complete the following:
[pic] Exponential form Expanded form
[pic] [pic]
(4) × (3)
b. Complete all the missing parts in the following table:
|(x[pic]y)m |Exponential form |Expanded form |
| | | |
|e.g. (2[pic]4)3 |(2)[pic][pic](4)1[pic]3 = (2) 3[pic](4)3 |(2)(2)(2)×(4)(4)(4) |
| | | |
|(3[pic]2) |(___)[pic][pic](___)[pic]=(__) [pic](__) |__________ × __________ |
| | | |
|(-3[pic]2)3 |(-3) 1[pic]3 [pic](2) = ___________ |__________ × __________ |
|(4[pic]3)-2 | |[pic] |
| |(___)[pic][pic](___)[pic]= (__) [pic] (__) | |
| | |[pic][pic] |
|(-2[pic]4) |(____) × (____) = _____×______ | |
| | | |
|(___ ×___) |[pic] |__________ × __________ |
c. Complete the Power of a Product Law:
When finding the power of a product you must __________the exponent outside the bracket by all the exponents inside the bracket.
5. Use the Power of a Quotient Law in the “Explore It” mode for the following exercise.
Move the slider bars as directed:
• m (purple) to 2
• x (red) to 3
• y (green) to 4
a. Use the above example in the “Explore It” mode to complete the following:
[pic] Exponential form Expanded form
[pic] [pic]
b. Complete all the missing parts in the following table:
|[pic] |Exponential form |Expanded form |
|e.g. [pic] |[pic] | [pic] |
| | | |
|[pic] |[pic]= [pic] | |
| | | |
| | |____________________ |
| | | |
|[pic] |[pic] = ______ | |
| | |____________________ |
| |[pic]= ________ | |
|[pic] | | |
| | |____________________ |
|[pic] | |[pic] |
| |[pic] = ______ | |
| | |____________________ |
c. Complete the Power of a Quotient Law:
When finding the power of a quotient you must _______the exponent outside the bracket by all the exponents inside the bracket.
6. Use the Zero Exponent Law in the “Explore It” mode for the following exercise.
Move the slider bar as directed:
• x (red) to 2
a. Use the above example in the “Explore It” mode to complete the following: [pic]
[pic] Exponential form Expanded form
[pic] ____ [pic]
___
b. Complete all the missing parts in the following table:
|(x)0 |Exponential form |Expanded form |
| | | [pic]= _____ |
|e.g. (4)0 |(4)0 = ____ | |
| | | [pic] |
|(___)0 |(y)0 = ____ | |
| |[pic] | |
|(-3)0 |(___) = ____ |[pic] |
| (___) | | |
| |(-6)0 = ____ |[pic] |
c. Complete the Zero Exponent Law:
The value of any base to the zero exponent is _____.
7. Use the Negative Exponent Law in the “Explore It” mode for the following exercise.
Move the slider bar as directed:
• n (orange) to -1
• x (red) to 2
.[pic]
a. Use the above example in the “Explore It” mode to complete the following:
[pic] Exponential form Expanded form
(2)-1 (2)-1
____ ____
b. Complete all the missing parts in the following table:
| | | |
|(x)-n |Exponential form |Expanded form |
| e.g. (4)-2 |[pic] | [pic] |
| | | |
|[pic] |[pic][pic] | |
| | |_______________ |
| |[pic] | |
|[pic] |[pic] | |
| | |_______________ |
c. Complete the Negative Exponent Law:
(x)-n is defined to be the ____________ of (x)n.
(inverse/opposite/reciprocal)
-----------------------
___________ ÷ ___________ ____________
___________ × ___________
___________ ÷ ___________
___________ ÷ ___________
___________ ÷ ___________
___________ ÷ ___________ ____________
___________ × ___________
___________ × ___________
___________ × ___________
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.