Exponents Jeopardy Game

Product Rule of Powers

100

7³ x 7⁴

=7⁷ or 49

200

A²B⁷C⁶ x AB⁵C⁴

=A²⁺¹B⁷⁺⁵C⁶⁺⁴

=A³B¹²C⁸

300

(x²y⁷z⁹)(x³y⁴z⁶)

=x²⁺³ y⁷⁺⁴ z⁹⁺⁶

=x⁵y¹¹z¹⁵

400

(F⁴⁵O⁹²R⁶⁵T²³N⁹⁰I⁷⁶T²¹E⁸⁴)(F¹²O³⁴R⁵²T⁷⁸N⁹⁹I³⁵T⁸E⁵³)

= F⁴⁵⁺¹² O⁹²⁺³⁴ R⁶⁵⁺⁵² T²³⁺⁷⁸ N⁹⁰⁺⁹⁹ I⁷⁶⁺³⁵ T²¹⁺⁸ E⁸⁴⁺⁵³

=F⁵²O¹²⁶R¹¹⁷T¹⁰¹N¹⁸⁹I¹¹¹T²⁹E¹³⁷

500

Q¹²W⁴⁵E⁷⁸R¹²⁰T¹³Y⁵⁴ x Q⁶⁷W⁸⁷E⁶⁷R²⁵⁸T²⁴Y³⁹

= Q¹²⁺⁶⁷ W⁴⁵⁺⁸⁷ E⁷⁸⁺⁶⁷ R^120+258 T¹³⁺²⁴ Y⁵⁴⁺³⁹

=Q⁷⁹W¹³²E¹⁴⁵R³⁷⁸T³⁷Y⁹³

Quotient Rule of Powers

100

5¹⁰y⁹ ÷ 5⁷y²

=5^10-7 y^9-2 

=5³y⁷

200

2⁶5⁷9⁹/2⁴59³

=2^6-4 5^7-1 9^9-3

=2²5⁶9⁶ 

300

6⁵2⁷b³c⁹/6²2⁴b⁸c⁷

=6^5-2 2^7-4 b^3-8 c^9-7

400

Y⁴⁵O²³U⁶⁷T⁸⁹U¹²B³⁹E⁵² / Y⁷⁸O³²U²⁹T¹²U⁹⁹B⁵⁶E⁶⁶

=Y^45-78 O^23-32 U^67-29 T^89-12 U^12-99 B^39-56 E^52-66

=U³⁸T⁷⁷/

Y³³O⁹U⁸⁷B¹⁷E¹⁴

500

9⁷⁰y⁵⁵x³³r⁷⁵⁰k⁶⁴³7²⁸⁸ ÷ 9⁴⁷y²⁴xr⁶⁰⁰k³⁵³7¹⁸⁰

= 9^70-47 y^55-24 x^33-1 r^750-600 k^643-3537^288-180

=9²³y³¹x³²r¹⁵⁰k²⁹⁰7¹⁰⁸

Negative Exponents

100

x^-5

=1/x⁵

200

4^-37²R^-8 x 4⁴7^-5R^-6

=4^{-3 + 4} 7^2+(-5) R^{-8 + -6}

=4¹1/

7³R¹⁴

300

4^-67^-5u^-4/d^-9o^-3g^-2

d⁹o³g²/4⁶7⁵u⁴

400

(8⁴5^-74⁹34^-27³)^-5

=8^{4 x -5} 5^{-7 x -5} 4^{9 x -5} 3^{1 x -5} 4^{-2 x -5} 7^{3 x -5}

=5³⁵4¹⁰/ 8²⁰4⁴⁵3⁵7¹⁵

500

E⁴⁵X^-54P²³O^-76N^-90E³¹²N⁶⁷T^-89S^-31/

E^-35X⁸²P^-14O^-57N⁹⁷E³N^-78T⁴²S^-81

=E^45-(-35) X^-54-82 P^23-(-14) O^-76-(-57) N^-90-97 E^312-3 

N^67-(-78) T^-89-42 S^-31-(-81)

=X¹³⁶P³⁷E³⁰⁹N¹⁴⁵S⁵⁰/

E⁸⁰O¹⁹N¹⁸⁷T¹³¹

Properties of Exponents

100

9⁴7³/9³7⁵

=9^4-3 7^3-5

=9¹1/7²

200

4⁵6⁷2²5⁰ x 4⁴6³2⁴5⁴

=46⁴15⁴/2²

300

u⁸i⁷o⁴p²a³ / u⁴i³o⁹p⁵a⁶

=u⁴i⁴1/o⁵p³a³

400

(4⁷5⁶x⁸y⁹ x 6⁵3⁴x⁷y²)³

=4^{3 x 3} 5^{6 x 3} x^{8 x 7} y^{9 x 3} 

x

6^{5 x 3} 3^{4 x 3} x^{7 x 3} y^{2 x 3}

⁼4²¹5¹⁸x⁴⁵y³³6¹⁵3¹²

500

(-6w²o⁵r^-6d⁰/5w⁵o^-3r²d)^-4

= -6^{1 x -4} w^{2 x -4} o^{5 x -4}  r^{-6 x -4}  d^{0 x -4}/

5^{1 x -4} w^{5 x -4} o^{-3 x -4} r^{2 x -4} d^{1 x -4}

= 5⁴w¹²r³²d⁴/-6⁴o³²

Miscellaneous Power Rules

100

8⁰

=(8)⁰

=1

200

(4⁵6²x³)⁰

=4^{5 x 0} 6^{2 x 0} x^{3 x 0}

=1

300

W⁵A⁸S²D⁹/W³A⁷S⁶D⁴

W²A1D⁵/S⁴

400

7¹⁶8⁽¹³⁾⁴9¹⁰3¹⁴5​⁽​​​¹⁸⁾⁴6¹⁷ x 7⁽¹³⁾​⁴​​​8¹²9²⁰3⁽¹⁷⁾⁴5¹⁶6¹⁵

=7⁶⁸8⁶⁴9³⁰3⁸²5⁹⁰6³²

500

1⁵2⁶3⁷a⁴b³c²/1⁹2⁸3⁷a⁵b³c⁷

=1/1⁴2²ac⁵