Properties of Exponents

All About Powers

100

Write 8⁵ in expanded form. 

8*8*8*8*8

200

Write the expression as a power.

x*x*x*x*x*x*x

x^7

300

Write 5³w⁵ in expanded form.

5*5*5*w*w*w*w*w

400

Write the expression as a power. 

3*3*a*a*a*b*b*b*b

3^2a^3b^4

500

Write the expression as a power.

-7*-7*-7*-7*y*y*y

(-7)^4y^3

Product/Quotient Rule

100

Simplify the expression.

a^5b^4*a^7b^10

a^12b^14

200

Simplify the expression.

(x^9y^12)/(x^4y^8)

x^5y^4

300

Simplify the expression.

(5x^8)(4x^3)

20x^11

400

Simplify the expression.

(30c^12d^14)/(5cd^2)

6c^11d^12

500

Simplify the expression.

(12x^10yz^-3)/(2x^-4y^8z^5)

(6x^14)/(y^7z^8)

Power of a Power Rule

100

Simplify the expression.

(14^5)^3

14^15

200

Simplify the expression.

7(w^11)^8

7w^88

300

Simplify the expression.

(a^3b^9c^5)^4

a^12b^36c^20

400

Simplify the expression.

((a^4b^8)/(c^6d))^3

(a^12b^24)/(c^18d^3

500

Simplify the expression.

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

36x^8y^4z^10

Negative/Zero Rule

100

Simplify the expression.

(ab)^0

1

200

Simplify the expression.

9^-2

1/81

300

Simplify the expression.

3x^-5

3/x^5

400

Simplify the expression.

(a^-3b^5c^-2)/(a^4b^3)

(b^2)/(a^7c^2)

500

Simplify the expression.

(9x^-5z^0)/(x^11y^-3)

(9y^3)/x^16

Mixed Problems

100

Write the expression as a power.

1/5*1/5*1/5*1/5

5^-4

200

Simplify the expression.

((20x^3y^-4z^30)/(12x^-4yz^7))^0

1

300

Simplify the expression.

(-4a^5b^3)^2/a^2

16a^8b^6

400

Simplify the expression.

(7a^4b^5)(2b^5c^2)^2

28a^4b^15c^4

500

Simplify the expression.

5x(2/x^-8)^3

40x^25