Exponents: Jeopardy Project By Sean Yi

Product Rule of Powers

100

4(4⁵)

4(4⁵)

4¹⁺⁵

4⁶

200

(2)(2³)(2⁴)

(2¹)(2³)(2⁴)

2¹⁺³⁺⁴

2⁸

300

(7)(5³)(2⁴)(7⁴)(3²)(2)

(7)(5³)(2⁴)(7⁴)(3²)(2)

(7¹⁺⁴)(5³)(2⁴⁺¹)(3²)

(7⁵)(5³)(3²)(2⁵)

400

(6²)(5⁴)(7²)(8⁴)(5³)(6)(8²)

(6²)(5⁴)(7²)(8⁴)(5³)(6)(8²)

(6²⁺¹)(5⁴⁺³)(7²)(8⁴⁺²)

(6³)(5⁷)(7²)(8⁶)

500

(3²)(4²)(8⁶)(7⁴)(2³)(8²)(3⁴)(4⁶)(2²)(4⁵)(3⁴)(7)(8⁶)

(3²)(4²)(8⁶)(7⁴)(2³)(8²)(3⁴)(4⁶)(2²)(4⁵)(3⁴)(7)(8⁶)

(3²⁺⁴⁺⁴)(4²⁺⁶⁺⁵)(8⁶⁺²⁺⁶)(7⁴⁺¹)(2³⁺²)

(3¹⁰)(4¹³)(8¹⁴)(7⁵)(2⁵)

Quotient Rule of Powers

100

3²/3

3²/3¹

3^2-1/1

3

200

7⁴/7²

7⁴/7²

7^4-2

7²

300

6³(7⁵)/6⁵(7³)

6³(7⁵)/6⁵(7³)

6^3-5(7^5-3)

6^-2(7²)

7²/6²

400

(3²)(5⁶)(2³)/(3⁶)(5)(2³)

(3²)(5⁶)(2³)/(3⁶)(5)(2³)

(3^2-6)(5^6-1)(2^3-3)

(3^-4)(5⁵)(1)

5⁵/3⁴

500

(7)(3¹⁰)(5⁶)(2⁵)(6⁷)/(7)(3¹⁰)(5⁴)(2)(6³)

(7)(3¹⁰)(5⁶)(2⁵)(6⁷)/(7)(3¹⁰)(5⁴)(2)(6³)

(7^1-1)(3^10-10)(5^6-4)(2^5-1)(6^7-3)

(1)(1)(5²)(2⁴)(6⁴)

(5²)(2⁴)(6⁴)

Negative Exponents

100

6^-2

6^-2

The negative exponent makes the reciprocal of the base

1/6²

200

7^-3(7^-4)

7^-3(7^-4)

7^-3+(-4)

7^-7

1/7⁷

300

(2/4)^-3

(2/4)^-3

(2^-3/4^-3)

(4³/2³)

400

(5*4/7*3)^-6

(5*4/7*3)^-6

(5^-6)(4^-6)/(7^-6)(3^-6)

(7⁶)(3⁶)/(5⁶)(4⁶)

500

(5*3*2/6*9*8)^-8

(5*3*2/6*9*8)^-8

(5^-8)(3^-8)(2^-8)/(6^-8)(9^-8)(8^-8)

(6⁸)(9⁸)(8⁸)/(5⁸)(3⁸)(2⁸)

Properties of Exponents(combination of rules)

100

4(4)²/4⁵

4¹(4)²/4⁵

4¹⁺²/4⁵

4³/4⁵

4^3-5

4^-2

1/4²

200

(4^-5)(4⁴)

(4^-5)(4⁴)

4⁴/4⁵

4^4-5

4^-1

1/4

300

(7)(5²)(5²)(7³)/(7³)(5⁶)

(7¹⁺³)(5²⁺²)/(7³)(5⁶)

(7⁴)(5⁴)/(7³)(5⁶)

(7^4-3)(5^4-6)

(7)(5^-2)

7/5²

(7)(5²)(5²)(7³)/(7³)(5⁶)

(7¹⁺³)(5²⁺²)/(7³)(5⁶)

(7⁴)(5⁴)/(7³)(5⁶)

(7^4-3)(5^4-6)

(7)(5^-2)

7/5²

400

(7²3)^-2(7*3³)²/(7⁶)(3⁵)

(7²*3)^-2(7*3³)²/(7⁶)(3⁵)

(7^2(-2))(3^-2)(7²)(3³⁽²⁾)/(7⁶)(3⁵)

(7^-4)(3^-2)(7²)(3⁴)/(7⁶)(3⁵)

(7²)(3⁴)/(7⁴)(7⁶)(3²)(3⁴)(3⁵)

(7²)(3⁴)/(7⁴⁺⁶)(3²⁺⁴⁺⁵)

(7²)(3⁴)/(7¹⁰)(3¹¹)

(7^2-10)(3^4-11)

(7^-8)(3^-7)

1/(7⁸)(3⁷)

500

(5²*4⁶*3)³(3²*5⁴*4*2)^-2/(5¹²)(6³)(4⁷)(2²)

(5²*4⁶*3)³(3²*5⁴*4*2)^-2/(5¹²)(6³)(4⁷)(2²)

(5²⁽³⁾)(4⁶⁽³⁾)(3³)(3^2(-2))(5^4(-2))(4^-2)(2^-2)/(5¹²)(6³)(4⁷)(2²)

(5⁶)(4¹⁸)(3³)(3^-4)(5^-8)(4^-2)(2^-2)/(5¹²)(6³)(4⁷)(2²)

(5⁶)(4¹⁸)(3³)/(5¹²)(6³)(4⁷)(2²)(3⁴)(5⁸)(4²)(2²)

(5⁶)(4¹⁸)(3³)/(5¹²⁺⁸)(6³)(4⁷⁺²)(2²⁺²)(3⁴)

(5^6-20)(4^18-9)(3^3-4)

(5^-14)(4⁹)(3^-1)

4⁹/(5¹⁴)(3¹)

Miscellaneous Power Rules

100

2⁰

2⁰​

any base with an exponent as a zero will equal 1.

1

​​​

200

(y²z³)²

(y²z³)²

y^2*2(z^3*2)

y⁴(z⁶)

300

2⁰(y²)x³/y⁵(x⁶)

2⁰(y²)x³/y⁵(x⁶)

1(y^2-5)(x^3-6)

(y^-3)(x^-3)

1/(y³)(x³)

400

(2⁰*y⁵)³(x²*y)²/(y⁶)(2²)(x³)

(2⁰*y⁵)³(x²*y)²/(y⁶)(2²)(x³)

(2⁰⁽³⁾)(y⁵⁽³⁾)(x²⁽²⁾)(y¹⁽²⁾)/(y⁶)(2²)(x³)

(1)(y¹⁵)(x⁴)(y²)/(y⁶)(2²)(x³)

(y¹⁵⁺²)(x⁴)/(y⁶)(2²)(x³)

(y^17-6)(x^4-3)/(2²)

(y¹¹)(x)/2²

500

(5⁰*2*y⁶)⁴(2⁰*5⁶*2²)³/(5⁰)(2⁴)(y¹⁰)(2⁴)

(5⁰*2*y⁶)⁴(2⁰*5⁶*2²)³/(5⁰)(2⁴)(y¹⁰)(2⁴)

(5⁰⁽⁴⁾)(2⁴)(y⁶⁽⁴⁾)(2⁰⁽³⁾)(5⁶⁽³⁾)(2²⁽³⁾)/(5⁰)(2⁴)(y¹⁰)(2⁴)

(1)(2⁴⁺⁶)(y²⁴)(1)(5¹⁸)/(1)(2⁴⁺⁴)(y¹⁰)

(2^10-8)(y^24-10)(5¹⁸)

(2²)(y¹⁴)(5¹⁸)