Quotient Quest Study Guide Tutorial Level
QUOTIENT QUEST
Mastering the Exponent Quotient Rule
Name: ______________________
Date: ______________________
Rule Decoded
The Quotient Rule
When dividing powers with the same base , keep the base and subtract the exponent of the denominator from the exponent of the numerator.
\[ \frac{x^a}{x^b} = x^{a-b} \]
Visual Proof
Expansion Chamber
Let's expand a division problem and cancel terms:
\[ \frac{x^5}{x^3} = \frac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x} \]
Cancel 3 matching pairs!
\[ = \frac{\not{x} \cdot \not{x} \cdot \not{x} \cdot x \cdot x}{\not{x} \cdot \not{x} \cdot \not{x}} = x^2 \]
Pro Tips
Level Rules
🎮 Base Match: Base must be identical. You can simplify \( \frac{x^5}{x^2} \) but NOT \( \frac{x^5}{y^2} \).
🎮 Invisible 1: If no exponent is shown, it is 1. \( y = y^1 \).
🎮 Zero Power: Any base to power of 0 equals 1. \( x^0 = 1 \).
Boss Encounters
Worked Examples
1
Problem \( \frac{y^9}{y^4} \)
Subtract \( y^{9 - 4} \)
Final Answer \( y^5 \)
2
Coefficients \( \frac{20w^{12}}{4w^{3}} \)
Divide Coefficients \( \frac{20}{4} \) and \( w^{12-3} \)
Final Answer \( 5w^9 \)
3
Multiple Bases \( \frac{a^{8}b^{5}}{a^{5}b} \)
Group Bases \( a^{8-5} \cdot b^{5-1} \)
Final Answer \( a^3 b^4 \)
Avoid!
Common Quest Pitfalls
Don't Divide Exponents:
Don't Subtract Coefficients:
LEVEL 1 COMPLETE READY FOR THE 20-QUESTION QUEST? SCORE: 00000
Quotient Quest Worksheet Level 1 & 2 Quests
QUOTIENT QUEST
Simplify each expression completely. Keep bases positive.
Name: ______________________
Date: ______________________
STAGES 1 & 2: BASIC & COEFFICIENTS HP: 100/100
Stage 1 Pixel Pioneers (Single Variables)
[ QUEST 01 ] 5 XP
\( \frac{x^7}{x^3} \)
[ QUEST 02 ] 5 XP
\( \frac{y^9}{y^2} \)
[ QUEST 03 ] 5 XP
\( \frac{a^{12}}{a^{10}} \)
[ QUEST 04 ] 10 XP
\( \frac{m^{15}}{m^5} \)
[ QUEST 05 ] 10 XP
\( \frac{k^4}{k} \)
Stage 2 Coefficient Clash (With Numbers)
[ QUEST 06 ] 15 XP
\( \frac{n^{20}}{n^{20}} \)
[ QUEST 07 ] 15 XP
\( \frac{6x^5}{2x^3} \)
[ QUEST 08 ] 15 XP
\( \frac{15y^8}{3y^4} \)
[ QUEST 09 ] 20 XP
\( \frac{24a^{10}}{8a^2} \)
[ QUEST 10 ] 20 XP
\( \frac{10b^7}{2b^6} \)
PAGE 1 / 2 MIDPOINT REACHED - FLIP PAGE TOTAL QUEST XP: 110/300
Level 3 & 4 Quests
QUOTIENT QUEST
Continue simplifying. Defeat the multi-variable bosses!
Name: ______________________
Date: ______________________
STAGES 3 & 4: MULTI-VARIABLES & CHALLENGES HP: 85/100
Stage 3 Multi-Variable Mayhem (Double Bases)
[ QUEST 11 ] 20 XP
\( \frac{36w^9}{9w^8} \)
[ QUEST 12 ] 20 XP
\( \frac{14p^{12}}{7p^{12}} \)
[ QUEST 13 ] 25 XP
\( \frac{x^5 y^4}{x^2 y^2} \)
[ QUEST 14 ] 25 XP
\( \frac{a^{10} b^7}{a^3 b^6} \)
[ QUEST 15 ] 25 XP
\( \frac{m^8 n^5}{m^4 n} \)
Stage 4 Final Bosses (Ultimate Challenges)
[ QUEST 16 ] 30 XP
\( \frac{18x^6 y^3}{6x^2 y^3} \)
[ QUEST 17 ] 30 XP
\( \frac{40a^5 b^{12}}{10a^3 b^{10}} \)
[ QUEST 18 ] 35 XP
\( \frac{21p^9 q^6}{7p^4 q^4} \)
[ QUEST 19 ] 40 XP
\( \frac{12a^9 b^8 c^4}{4a^5 b^4 c^4} \)
[ QUEST 20 ] 40 XP
\( \frac{100x^{15} y^9}{25x^{10} y^9} \)
PAGE 2 / 2 FINAL LEVEL COMPLETE - CHIP TO WIN TOTAL QUEST XP: 300/300
Quotient Quest Answer Key Teacher Resource
ANSWER KEY: QUOTIENT QUEST
Detailed solutions and marking guide for Pages 1 & 2.
MASTER KEY
STAGES 1 & 2 SOLUTIONS TOTAL QUESTIONS: 20
Stage 1 Pixel Pioneers (Single Variables)
[ QUEST 01 ] 5 XP
\( \frac{x^7}{x^3} \)
\( x^{7-3} = \) \( x^4 \)
[ QUEST 02 ] 5 XP
\( \frac{y^9}{y^2} \)
\( y^{9-2} = \) \( y^7 \)
[ QUEST 03 ] 5 XP
\( \frac{a^{12}}{a^{10}} \)
\( a^{12-10} = \) \( a^2 \)
[ QUEST 04 ] 10 XP
\( \frac{m^{15}}{m^5} \)
\( m^{15-5} = \) \( m^{10} \)
[ QUEST 05 ] 10 XP
\( \frac{k^4}{k} \)
\( k^{4-1} = \) \( k^3 \)
Stage 2 Coefficient Clash (With Numbers)
[ QUEST 06 ] 15 XP
\( \frac{n^{20}}{n^{20}} \)
\( n^{20-20} = n^0 = \) \( 1 \)
[ QUEST 07 ] 15 XP
\( \frac{6x^5}{2x^3} \)
\( \frac{6}{2} \cdot x^{5-3} = \) \( 3x^2 \)
[ QUEST 08 ] 15 XP
\( \frac{15y^8}{3y^4} \)
\( \frac{15}{3} \cdot y^{8-4} = \) \( 5y^4 \)
[ QUEST 09 ] 20 XP
\( \frac{24a^{10}}{8a^2} \)
\( \frac{24}{8} \cdot a^{10-2} = \) \( 3a^8 \)
[ QUEST 10 ] 20 XP
\( \frac{10b^7}{2b^6} \)
\( \frac{10}{2} \cdot b^{7-6} = \) \( 5b \)
PAGE 1 SOLUTIONS CONFIRM ALL STEPS SHOWN ABOVE LEVELS 1 & 2 FIXED
Teacher Resource
ANSWER KEY: QUOTIENT QUEST
Detailed solutions and marking guide for Stage 3 & 4.
MASTER KEY
STAGES 3 & 4 SOLUTIONS TOTAL QUESTIONS: 20
Stage 3 Multi-Variable Mayhem (Double Bases)
[ QUEST 11 ] 20 XP
\( \frac{36w^9}{9w^8} \)
\( 4 \cdot w^{9-8} = \) \( 4w \)
[ QUEST 12 ] 20 XP
\( \frac{14p^{12}}{7p^{12}} \)
\( 2 \cdot p^0 = 2(1) = \) \( 2 \)
[ QUEST 13 ] 25 XP
\( \frac{x^5 y^4}{x^2 y^2} \)
\( x^{5-2} y^{4-2} = \) \( x^3 y^2 \)
[ QUEST 14 ] 25 XP
\( \frac{a^{10} b^7}{a^3 b^6} \)
\( a^{10-3} b^{7-6} = \) \( a^7 b \)
[ QUEST 15 ] 25 XP
\( \frac{m^8 n^5}{m^4 n} \)
\( m^{8-4} n^{5-1} = \) \( m^4 n^4 \)
Stage 4 Final Bosses (Ultimate Challenges)
[ QUEST 16 ] 30 XP
\( \frac{18x^6 y^3}{6x^2 y^3} \)
