Exponent Rules

Multiplying

100

x^3*x^6

x^9

200

6^12*6^8

6^20   

300

2x^5*4x^7

8x^12

400

(4f^8m^3)(4f^4m^2)

16f^12m^5

500

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

(21s^11)/p^2

21s^11p^-2 

 Not Fully Simplified

Dividing

100

4^5/4^2

4^3

200

x^7/x^3

x^4

300

(24y^10)/(4y^3)

6y^7

400

(-30x^5y^9)/(5x^4y)

-6xy^8

500

(20m^4x^3)/(2m^8x)

(10x^2)/m^4x

10m^-4x^2 

  Not Fully Simplified 

Power of a Power

100

(2^3)^4

2^12

200

(d^2)^4

d^8

300

(3b^4)^3

27b^12

OR

3^3b^12

400

(-4w^5xy^2)^4

256w^20x^4y^8

OR

(-4)^4w^20x^4y^8

500

(7a^10b^4)^-2

1/(49a^20b^8)

OR

7^-2a^-20b^-8

Mixed Bag

100

Evaluate 

54^1

54

200

(2^3*4^4)^0

1

  Any number (except 0) to the power of 0 is 1.

300

Simplify with Positive Exponents 

(a^-5)/(a^-3) 

1/(a^2)

400

Simplify with positive exponents

(21x^-4y^2)/(7x^2y^-4)

(3y^6)/x^6

500

Write the following expression with positive exponents 

(x^5y^-3)/(b^-2z^4)

(x^5b^2)/(y^3z^4)

Vocabulary and More

100

What is the Base and what is the Exponent the following expression?

8^4

Base: 8

Exponent: 4

200

What is the rule when Multiplying like bases? 

for example:

2^5*2^3

What is the rule when Dividing like bases? 

for example:

(5^7)/5^4

What is the rule when Take the Power of a Power with like bases? 

for example:

(4^3)^2

Keep the base, ADD the exponents. 

Keep the base, SUBTRACT the exponents

Keep the base, MULTIPLY the exponents

300

Write the following expression in Exponential, Expanded and Evaluated Forms:

Negative 5 to the power of 4

Exponential 

(-5)^4

Expanded

(-5)(-5)(-5)(-5)

Evaluated 

625

400

What does any number to the zero power equal?

What does any number to the 1st power equal? 

1

Itself

500

Simplify

((y^-2)/3)^3

1/(3^3y^6

OR

1/(27y^6)