Room 420 - Exponent Laws

Product Rule

100

f³ x f¹⁰

What is f¹³

200

m⁵ x m^? = m²

m = -3

300

7⁴ x 7¹⁰ x 5³ x 7^-2

What is 5³ x 7¹²

400

5mk * 4m² * k⁸ *k^-4

What is 20m³k⁵

500

9x^4y^5*10x^3y^2

90x^7y^7

Power Rule

100

(17²)²

What is 17⁴

200

(5t⁴)³

5^3t^12

300

(1/2)^3

What is 

1/2^3

400

((-2)^5)^-3

What is 

(-2)^-15

500

(2^2/5^3)^-2

What is 

2^-4/5^-6

or 5^6/2^4

Zero and Negative Exponents

100

2⁰

What is 1

200

5m^0

What is 5

300

18x^3*2x^0

What is 

36x^3

400

(3y^3)^0

What is 1

500

1/2p^6 *10p^0*p^-3

What is 

5p^3

Quotient of Powers

100

5^9/5^2

What is 

5^7

200

(4m^7)/(2m^4

What is 

2m^3

300

(36h^6)/(12h^10)

What is 

3/h^4

400

(4^2)/(2^2)

What is 

2^2

500

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

What is 

7/(5d^7)

Application

100

Harrison has $120 in his bank account. Express the prime factorization of this number. 

What is 

2^3xx3xx5

200

Express the number 1.23 in expanded form. 

What is 

(1xx10^0)+(2xx10^-1) +(3xx10^-2)

300

Today's date is October 5. Express this number as an exponential expression. 

Multiple correct answers such as

5^3/5^2

400

Create three exponential expressions that have a quotient of 

3^4

Many probable outcome

500

Xavier stated that this expression contains a negative exponent in the final simplification. Is he correct. 

4k^13 xx(4k^-4)^2

No.