Jeopardy With Powers by Drew

Exponent Laws I

100

What is the name of the exponent law showed below:

a^m x aⁿ = a^m+n

What is Product Law

200

What is the name of the exponent law showed below:

(a^m )ⁿ= a^mn

What is Power Law

300

What is the name of the exponent law showed below:

a⁰ = 1

What is Zero Exponent Law

400

What is the name of the exponent law showed below:

a^m / aⁿ = a^m-n

What is Quotient Law

500

What is the name of the exponent law showed below:

a^-x = 1/a^x

What is Negative Exponent Law

Exponent Laws II

100

Evaluate.

(a⁹ x a³)/ a⁶

(a⁹⁺³)/a⁶ = a¹²/a⁶

a^12-6= a⁶

200

Evaluate.

(x²)³ / x⁶

(x^2x3)/x⁶ = x⁶/x⁶

x^6-6 = x⁰ = 1

300

Evaluate.

((m³)³)³

(m^3x3)³ = (m⁹)³ = m^9x3

=m²⁷

400

Evaluate.

(a⁵)x[(a²)³/ a¹⁰]

a⁵ x [ a^2x3 / a¹⁰ ] = a⁵ x [ a⁶ / a¹⁰ ]

a⁵ x [ a^6-10 ] = a⁵ x a^-4 = a^5+(-4)= a¹ 

= a

500

Evaluate.

((y⁴ / y^-2) / (y^-4 / y^-3) )³

((y^{4 -(-2)}) / (y^{-4 -(-3)}) )³ 

((y⁴⁺²) / (y^-4+3) )³ = ( y⁶ / y^-1 )³

(y^6-(-1))³ = (y⁶⁺¹)³ = (y⁷)³ = y^7x3 = y²¹ 

Mental Workout II

100

Evaluate using exponent laws, leave answer as a number.

-(-3^-1)^-3

-(-3^-1x-3) = -(-3³) = -(-27) 

= 27

200

Evaluate using exponent laws, leave answer as a number.

((9²)³ / 9³)^-2 x 3²

(9^2x3 / 9³)^-2 x 3² = (9⁶ / 9³)^-2 x 3² = (9^6-3)^-2 x 3²

(9³)^-2 x 3² = 9^3x(-2) x 3² = 9^-6 x 3² = 9^-6 x 9 = 9^-6+1

=9^-5  = 1 / (9⁵) = 1 / 59,049

300

Evaluate using exponent laws, leave answer as a number.

(2²)² x (2 / 2^-1)^-2

(2^2x2)x(2 / 2^-1)^-2 = 2⁴ x (2^1-(-1))^-2 = 2⁴ x (2¹⁺¹)^-2

=2⁴ x (2²)^-2 = 2⁴ x 2^-4 = 2^4+(-4) 

= 2⁰ = 1

400

Evaluate using exponent laws, leave answer as a number.

3³ x (3^-1 x 3^-2)^(2/3)

3³ x (3^-1+(-2))^(2/3)=3³ x (3^-3)^(2/3) = 3³ x 3^{(-3 x 2/3)}

3³ x 3^-2 = 3^3+(-2) = 3¹ = 3

500

Evaluate using exponent laws, leave answer as a number.

2⁴ / (2² x (2^-1)²)

2⁴ / (2² x (2^-1x2) = 2⁴ / (2² x 2^-2) 

2⁴ / (2^2+(-2)) = 2⁴ / (2^2-2) = 2⁴ / 2⁰ = 2⁴ / 1

= 2⁴ = 16

Paper may be required

100

Evaluate using exponent laws, leave answer as a number.

(3)³ x (9^(7/8) / 9^(1/4) x 9^(3/8))

(3)³ x (9^{(7/8 - 1/4 + 3/8)})=(3)³ x 9^{(7/8 - 2/8 + 3/8)}

(3)³ x 9^{((7 - 2 +3)/8)} = (3)³ x 9^(8/8) = (3)³ x 9¹

3³ x 3² = 3³⁺² = 3⁵ = 243

200

Evaluate using exponent laws, leave answer as a number.

(2^-4) x (4³ / 4^-5)^(1/2)

(2^-4) x (4^3-(-5))^(1/2) = 2^-4 x (4³⁺⁵)^(1/2)=2^-4 x (4⁸)^1/2

2^-4 x 4^8x(1/2) = 2^-4 x 4^(8/2) = 2^-4 x 4⁴ = 2^-4 x (2²)⁴

= 2^-4 x 2^2x4 = 2^-4 x 2⁸ = 2^-4+8 = 2⁴ = 16 

300

Evaluate using exponent laws, leave answer as a number.

3⁷ / (3^(1/2) x 3^(1/5))¹⁰

3⁷ / (3^(1/2)+(1/5))¹⁰ = 3⁷/(3^5/10+2/10)¹⁰ 

3⁷/(3^(5+2)/10)¹⁰ = 3⁷/(3^7/10)¹⁰ = 3⁷/3^7/10x10

3⁷/3⁷ = 3^7-7 = 3⁰ = 1

400

Evaluate using exponent laws, leave answer as a number.

((2^-(1/2))^-(1/3))⁶ x (2^-1 / 2²)

(2^{(-(1/2) x -(1/3))})⁶ x (2^-1 / 2²) = (2^1/6)⁶ x (2^-1/2²)

(2^(1/6 x 6))x(2^-1/2²) = 2¹ x (2^-1-2)= 2¹ x 2^-3= 2^1+(-3) 

= 2^-2 = 1/2² = 1/4

500

Evaluate using exponent laws, leave answer in power form

(1/3²) x (9²/3)^-1/3

(3^-2) x ((3²)²/3)^-1/3 = 3^-2 x ((3^2x2)/3)^-1/3

3^-2 x ((3⁴)/3)^-1/3 = 3^-2 x (3^4-1)^-1/3 = 3^-2 x (3³)^-1/3

3^-2 x (3^{(3 x -1/3)}) = 3^-2 x 3^-1 = 3^-2+(-1) = 3^-3

Mental Workout I

100

Evaluate using exponent laws, leave answer as a number.

(3^1/2 x 3¹)²

(3^1/2+1)² = (3^{1/2 + 2/2})² = (3^3/2)²

=3³ = 27

200

Evaluate using exponent laws, leave answer as a number.

(2^-2 x 2³)/(2² / 2^-2)⁰ 

(2^-2 x 2³) / (1) = 2^-2+3 / 1

= 2¹ = 2

300

Evaluate using exponent laws, leave answer as a number.

(5²)^(1/2) / (5⁴)^1/2

5^{(2 x 1/2)} / 5^{(4 x 1/2)} = 5¹ / 5² = 5^1-2 

= 5^-1 = 1/5

400

Evaluate using exponent laws, leave answer as a number.

(2^1/2 x (2^2/8)²) / 2^-1

(2^1/2 x (2^2/8x2) / 2^-1 = (2^1/2 x 2^4/8) / 2^-1 

= 2^1/2+4/8 / 2^-1 = 2¹ / 2^-1

=2^1-(-1) = 2¹⁺¹ = 2² = 4

500

Evaluate using exponent laws, leave answer as a number.

2⁴ / (2² x 2)² 

2⁴ / (2²⁺¹)² = 2⁴ / (2³)² = 2⁴ / 2^3x2 

= 2⁴ / 2⁶ = 2^4-6 

= 2^-2 = 1/4