Index Laws #2

Multiplication Law

100

b^3 × b^2

b^5

200

k^7 × k

k^8

300

 p^4q^2 × p^3 

p^7q^2

400

5m^2n^3 × 2m^4n

10m^6n^4

500

6a^3b × 3a^2b^4c

18a^5b^5c

Division Law

100

a^6 ÷ a^4

a^2

200

t^9 ÷ t^3

t^6

300

r^5s^4 ÷ r^2s

r^3s^3

400

(15x^8y^5) / (5x^3y^2)

3x^5y^3

500

(24p^7q^6) / (6p^4q^2)

4p^3q^4

Power of a Power

100

(3^2)^3

3^6

200

(y^3)^4

y^12

300

(ab^2)^3

a^3b^6

400

(4x^2y)^2

16x^4y^2

500

(5m^3n^2)^2

25m^6n^4

Zero Index Law

100

5^0

1

200

x^0

1

300

x^0 + z^0 +y^0 

3

400

9m^0 -4x^0 

5

500

12m^0n^2k

12n^2k

Combining Index Laws

100

(x^3)^2 ÷ x^4

x^2

200

(a^2)^3 × a

a^7

300

(m^4n)^2 / m^3

m^5n^2

400

((2x^2y)^2 × x) / (4x^2)

x^3y^2

500

(3a^3b^2)^2 ÷ 3ab^3

3a^5b

Negative Indices

100

Simplify  5^-1 

1/5

200

Simplify 

x^-2

1/x^2

300

Simplify  3a^-1 

3/a

400

Simplify  4x^2y^-3 

(4x^2)/y^3

500

Simplify  (2a^-2b)^2 

(4b^2)/a^4