PROPERTIES OF EXPONENTS WORKSHEET

Problem 1 :

Simplify : 

2m² ⋅ 2m³

Problem 2 :

Simplify :

m⁴ ⋅ 2m^-3

Problem 3 :

Simplify :

(4a³)²

Problem 4 :

Simplify : 

(x³)⁰

Problem 5 :

Simplify : 

4a³b² ⋅ 3a⁴b³

Problem 6 :

Simplify : 

r²/2r³

Problem 7 :

Simplify : 

4x⁰y²z³ / 4x

Problem 8 :

Simplify :

(2xy⁴)⁴(xy)⁵

Problem 9 :

Simplify :

x^-4 / x^-9

Problem 10 :

Simplify :

x^-1 / 4x⁴

Problem 11 :

Simplify :

(x²y^-1)⁴

Problem 12 :

Simplify :

x²y³ ⋅ x³y²

Solutions

Problem 1 :

Simplify : 

2m² ⋅ 2m³

Solution :

2m² ⋅ 2m³  =  2m² ⋅ 2m³

2m² ⋅ 2m³  =  4m⁽²⁺³⁾

2m² ⋅ 2m³  =  4m⁵

Problem 2 :

Simplify :

m⁴ ⋅ 2m^-3

Solution :

m⁴ ⋅ 2m^-3  =  m⁴ ⋅ 2m^-3

m⁴ ⋅ 2m^-3  =  2m^{(4 - 3)}

m⁴ ⋅ 2m^-3  =  2m¹

m⁴ ⋅ 2m^-3  =  2m

Problem 3 :

Simplify :

(4a³)²

Solution :

(4a³)²  =  4²(a³)²

(4a³)²  =  16a⁽³⁾⁽²⁾

(4a³)²  =  16a⁶

Problem 4 :

Simplify : 

(x³)⁰

Solution :

(x³)⁰  =  1

Problem 5 :

Simplify : 

4a³b² ⋅ 3a⁴b³

Solution :

4a³b² ⋅ 3a⁴b³  =  12a³⁺⁴b²⁺³

4a³b² ⋅ 3a⁴b³  =  12a⁷b⁵

Problem 6 :

Simplify : 

r²/2r³

Solution :

r² / 2r³  =  r² / 2r³

r² / 2r³  =  (1/2) r^(2-3)

r² / 2r³  =  (1/2) r^-1

r² / 2r³  =  1 / 2r

Problem 7 :

Simplify : 

4x⁰y²z³ / 4x

Solution :

4x⁰y²z³ / 4x  =  4(1)y²z³ / 4x

4x⁰y²z³ / 4x  =  y²z³ / x

Problem 8 :

Simplify :

(2xy⁴)⁴(xy)⁵

Solution :

(2xy⁴)⁴(xy)⁵  =  2⁴x⁴ (y⁴)⁴ x⁵ y⁵

(2xy⁴)⁴(xy)⁵  =  16x⁴y¹⁶x⁵y⁵

(2xy⁴)⁴(xy)⁵  =  16x⁽⁴⁺⁵⁾y⁽¹⁶⁺⁵⁾

(2xy⁴)⁴(xy)⁵  =  16x⁹y²¹

Problem 9 :

Simplify :

x^-4 / x^-9

Solution :

 x^-4 / x^-9  =  x^-4 / x^-9

x^-4 / x^-9  =  x^{(-4 + 9)}

x^-4 / x^-9  =  x⁵

Problem 10 :

Simplify :

x^-1 / 4x⁴

Solution :

x^-1 / 4x⁴  =  (1/4)x^-1-4

x^-1 / 4x⁴  =  (1/4)x^-5

x^-1 / 4x⁴  =  1/4x⁵

Problem 11 :

Simplify :

(x²y^-1)⁴

Solution :

(x²y^-1)⁴  =  (x²)⁴(y^-1)⁴

(x²y^-1)⁴  =  x⁸y^-4

(x²y^-1)⁴  =  x⁸ / y⁴

Problem 12 :

Simplify :

x²y³ ⋅ x³y²

Solution :

x²y³ ⋅ x³y²  =  x²⁺³y³⁺²

x²y³ ⋅ x³y²  =  x⁵y⁵

x²y³ ⋅ x³y²  =  (xy)⁵

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