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:
Exponential form
Expanded form
4 2 × 43
4 2 × 43
(4)(4) × ______
____________
_____
(__) 2 + 3
(4)
___
b. Complete all the missing parts in the following table:
xm × xn
Exponential form
Expanded form
Eg. 31 × 34
(3)1+4 = (3)5
(3) × (3)(3)(3)(3)
52 × 5
(5)2+3 = ______
___________ × ___________
(-4)
× (__)
+
(___)
= ______
1
× (3)(3)(3)(3)
(3)(3)
Eg. (3)-2 × (3)4
(3)
= (3)
(-2)-1 × (__)-3
(-2)
+
(___)
(-6)3+2 = ______
×(___)
(2)4 × (2)-3
-2+4
(2)
+
(-4)(-4) × (-4)(-4)
2
= ______
= ______
___________ × ___________
___________ × ___________
___________ × ___________
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
Page 1 of 8
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:
Exponential form
Expanded form
45 ÷ 43
45 ÷ 43
(4)(4)(4)(4)(4) ÷ (4)(4)(4)
__________
_____
(_) 5− 3
(4)
___
b. Complete all the missing parts in the following table:
xm
÷ xn
Exponential form
Eg.
34 ÷ 31
(3) 4−1 = (3) 3
53 ÷ 5
(5) 3− 2 = ____
(-3)3 ÷ (-3)2
( −3)
(-4)
÷ (___)
÷ (3)2
(3)
÷ (__)-3
(-2)
Eg. (3)-4
(-2)-1
−4 − 2
(3)(3)(3)(3) ÷ (3)
−
= (3)
−
___________ ÷ ___________
= ____
−
(___)
Expanded form
= _____
−6
= ____
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
___________ ÷ ___________
( −4)( −4)( −4)( −4) ÷ (−4)( −4)
1
÷ (3)(3)
(3)(3)(3)(3)
___________ ÷ ___________
Page 2 of 8
(__)-3
(2)3
÷ (__)2
(-6)-3-2 = _____
÷ (2)-3
−
(-2)
___________ ÷ ___________
= ____
___________ ÷ ___________
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:
Exponential form
Expanded form
(4 2 ) 3
(4 2 ) 3
(___) 2× 3
(__) ×(__) ×(__)
________________
____________
(__)
____
b. Complete all the missing parts of the following table:
(xm )n
Exponential form
Expanded form
e.g. (23 )2
(2) 3×2 = (2) 6
(2)(2)(2)(2)(2)(2)
(52)
(5) 2× 2 = _____
____________________
((-3)3)2
(-3)
((-4)
)2
(-4)
×
×
= _____
= _____
____________________
(-4)(-4)(-4)(-4)
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
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e.g.(-3)-4)2
(−3) −4× 2 = (−3) −8
((4)-3 )-2
(4)
((-2)-1 )-3
(___)
×
= _____
_________________________
((3)2 ) -2
(___)
×
= _____
_________________________
×
⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞
⎜
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎟
⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠⎝ − 3 ⎠
= _____
_________________________
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:
Exponential form
(4 × 3) 2
(4)1× 2 × (3)1× 2
(4)
Expanded form
(4 × 3) 2
(_____) × (____)
_______________
× (3)
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
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b. Complete all the missing parts in the following table:
(x × y)m
Exponential form
e.g. (2 × 4)3
(2)
(3 × 2)
(___)
(-3 × 2)3
(-3) 1 × 3
1×3
× (4)1 × 3 = (2) 3 × (4)3
Expanded form
(2)(2)(2)×(4)(4)(4)
× (___) 1×3 =(__) × (__)
__________ × __________
× (2)
__________ × __________
1×3
= ___________
(4 × 3)-2
(___)
(-2 × 4)
(____)
(___ ×___)
(−3)1× 2 × (2)1× 2 = (−3) 2 × (2) 2
1× −2
× (___)
1× −2
× (__)
= (__)
× (____)
= _____×______
⎛ 1 ⎞⎛ 1 ⎞ ⎛ 1 ⎞⎛ 1 ⎞
⎜ ⎟⎜ ⎟ × ⎜ ⎟⎜ ⎟
⎝ 4 ⎠⎝ 4 ⎠ ⎝ 3 ⎠⎝ 3 ⎠
⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞ ⎛ 1 ⎞⎛ 1 ⎞⎛ 1 ⎞
⎜
⎟⎜
⎟⎜
⎟ × ⎜ ⎟⎜ ⎟⎜ ⎟
⎝ − 2 ⎠⎝ − 2 ⎠⎝ − 2 ⎠ ⎝ 4 ⎠⎝ 4 ⎠⎝ 4 ⎠
__________ × __________
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:
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
Page 5 of 8
Exponential form
⎛3⎞
⎜ ⎟
⎝4⎠
Expanded form
2
(__)1× 2
⎛3⎞
⎜ ⎟
⎝4⎠
(__)1× 2
(3)1
(4)1
2
×
(__)1
(__)1
____
b. Complete all the missing parts in the following table:
⎛x⎞
⎜⎜ ⎟⎟
⎝ y⎠
⎛2⎞
e.g. ⎜ ⎟
⎝4⎠
Exponential form
(2)1× 3
(4)1× 3
(3)1× 4
⎛3⎞
⎜ ⎟
⎝2⎠
⎛ −3⎞
⎜
⎟
⎝ 4 ⎠
3
m
(2)1× 4
3
=
(−3)
( 4)
(−4)1× 2
⎛
⎞
⎜⎜
⎟⎟
⎝ ___ ⎠
⎛ −3⎞
⎜
⎟
⎝−4⎠
=
(−3)1× 2
( 2) 3
( 4) 3
(3)
( 2)
= ______
Expanded form
1
1
1
⎛2⎞ ⎛2⎞ ⎛2⎞
⎜ ⎟ ×⎜ ⎟ ×⎜ ⎟
⎝4⎠ ⎝4⎠ ⎝4⎠
____________________
____________________
= ________
____________________
−2
(−3)
(−4)
= ______
____________________
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
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
Page 6 of 8
a. Use the above example in the “Explore It” mode to complete the following:
Exponential form
20 =
Expanded form
( 2) 0
2
2
____
___
b. Complete all the missing parts in the following table:
(x)0
e.g. (4)0
0
Exponential form
(4)0 = ____
0
(___)
(y) = ____
(-3)0
(___)
(___)
(-6)0 = ____
= ____
Expanded form
4
= _____
4
y
= _____
y
(__)
= ____
(__)
(__)
= ____
(__)
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
.
a. Use the above example in the “Explore It” mode to complete the following:
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
Page 7 of 8
Exponential form
(2)-1
Expanded form
(2)-1
____
____
b. Complete all the missing parts in the following table:
(x)-n
-2
e.g. (4)
(5) −3
(−6) −2
Exponential form
1
1
=
(4)(4) (4) 2
1
1
=
(__)(__)(__) (__) 3
1
1
=
(__)(__) (__)
Expanded form
⎛ 1 ⎞⎛ 1 ⎞
⎜ ⎟⎜ ⎟
⎝ 4 ⎠⎝ 4 ⎠
_______________
_______________
c. Complete the Negative Exponent Law:
(x)-n is defined to be the ____________ of (x)n.
(inverse/opposite/reciprocal)
Junior High Math Interactives
©2006 Alberta Education (www.LearnAlberta.ca)
Number / Power Properties / Object Interactive / Print Activity
Page 8 of 8