SIMPLIFYING EXPRESSIONS WITH POWERS

We can use the following properties of exponents to simplify expressions with powers. 

Solved Examples

Example 1 :

Simplify : 

(x3)2

Solution : 

=  (x3)2

=  x 3 ⋅ 2

=  x 6

Example 2 :

Simplify :

x⋅ x5

Solution :  

=  x⋅ x5

=  x3 + 5

=  x 8

Example 3 :

Simplify : 

m0 · m-3 · m5

Answer : 

=  m0 · m-3 · m5

=  1 · m-3 + 5

=  m2

Example 4 :

Simplify : 

x/ x5

Solution : 

=  x/ x5

=  x8 - 5

=  x3

Example 5 :

Simplify : 

4x/ 8x7

Solution : 

=  4x/ 8x7

=  x/ 2x7

=  x5 - 7 / 2

=  x-2 / 2

=  1 / (2x2)

Example 6 :

Simplify : 

(121m6)1/2

Solution :

=  (121m6)1/2

=  (11 ⋅ 11 ⋅ m6)1/2

=  (11⋅ m6)1/2

=  (112)1/2 ⋅ (m6)1/2

=  11⋅ 1/2 ⋅ m⋅ 1/2

=  111 ⋅ m3

=  11m3

Example 7 :

Simplify : 

(9n4)1/2

Solution :

=  (9n4)1/2

=  (3⋅ n4)1/2

=  (32)1/2 ⋅ (n4)1/2

=  3⋅ 1/2 ⋅ n⋅ 1/2

=  31 ⋅ n2

=  3 ⋅ n2

=  3n2

Example 8 :

Simplify : 

(8x3y6)1/3

Solution :

=  (8x3y6)1/3

=  (2⋅ x⋅ y6)1/3

=  (23)1/3 ⋅ (x3)1/3 ⋅ (y6)1/3 

=  2⋅ 1/3 ⋅ x⋅ 1/3 ⋅ y⋅ 1/3 

=  21 ⋅ x⋅ y2

=  2xy2

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