Exponent Glitch Coloring Worksheet
Exponent Glitch Color by Number
Power & Product Rules of Exponents with Coefficients
Name:
Date:
Period:
Rule Recap:
Product: \( x^a \cdot x^b = x^{a+b} \)
Power: \( (x^a)^b = x^{a \cdot b} \)
Coefficients: \( (c \cdot x^a)^b = c^b \cdot x^{a \cdot b} \)
Directions: Simplify each of the 10 expressions below and write your steps in the work line. Find your answer among the choices to reveal which color matches that problem number, then flip to Page 2 to color in the Confused Robot!
Problem 1 Product Rule
\( x^4 \cdot x^5 \)
Work: x^(4+5)
\( x^{20} \)
Red
\( x^9 \)
Yellow
\( x^1 \)
Blue
Problem 2 Power Rule
\( (y^3)^4 \)
Work: y^(3·4)
\( y^{12} \)
Light Blue
\( y^7 \)
Orange
\( y^{34} \)
Purple
Problem 3 Coefficients + Product
\( (3a^2)(4a^5) \)
Work: (3·4) a^(2+5)
\( 7a^7 \)
Green
\( 12a^{10} \)
Pink
\( 12a^7 \)
Orange
Problem 4 Power of Product
\( (2m^4)^3 \)
Work: 2³ · m^(4·3)
\( 6m^{12} \)
Yellow
\( 8m^{12} \)
Purple
\( 2m^{12} \)
Red
Problem 5 Two Variables
\( (5x^3 y^2)(2x^4 y^6) \)
Work: (5·2) x^(3+4) y^(2+6)
\( 10x^7 y^8 \)
Red
\( 7x^7 y^8 \)
Gray
\( 10x^{12} y^{12} \)
Green
Problem 6 Power of 2 Variables
\( (3p^2 q^5)^2 \)
Work: 3² · p^(2·2) q^(5·2)
\( 6p^4 q^{10} \)
Blue
\( 9p^4 q^7 \)
Orange
\( 9p^4 q^{10} \)
Green
Problem 7 Three Factors
\( (2k)(3k^4)(k^3) \)
Work: (2·3·1) k^(1+4+3)
\( 6k^7 \)
Pink
\( 6k^8 \)
Dark Blue
\( 5k^8 \)
Yellow
Problem 8 Power with Coefficient
\( (4w^6)^2 \)
Work: 4² · w^(6·2)
\( 16w^{12} \)
Gray
\( 8w^{12} \)
Dark Blue
\( 16w^8 \)
Purple
Problem 9 Power Then Product
\( (x^3)^2 \cdot x^4 \)
Work: x^(3·2) · x^4 = x^(6+4)
\( x^9 \)
Brown
\( x^{24} \)
Red
\( x^{10} \)
Pink
Problem 10 Multi-Step Challenge
\( 2(3n^3)^2 \)
Work: 2 · 3² · n^(3·2) = 2 · 9n^6
\( 36n^6 \)
Green
\( 18n^6 \)
Teal
\( 12n^6 \)
Sky Blue
Color Discovery: Solve each problem to find its color code. Color every region with that number on Page 2!
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Color by Number
Name:
Date:
10 1 1 4 9 9 4 8 5 10 1 7 1 1 1 5 10 8 4 4 4 4 8 8 8 2 1 5 9 9 3 2 7 8 8 3 3 10 10 2 6 3 5 6 7 3 7 10 7 3 7 10 1 1 2 9 10 10 6 6 1 3 3 7 7 4 4 7 7 8 4 8 4
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