# MULTIPLICATION WITH RATIONAL EXPONENTS

Example 1 :

Evaluate :

3x1/2x2/3

Solution :

=  3x1/2 ⋅ x2/3

=  3x1/2 + 2/3

=   3x3/6 + 4/6

=   3x7/6

Example 2 :

Evaluate :

(3√x⋅ 6√x4)-3

Solution :

=  (3√x⋅ 6√x4)-3

=  [(x2)1/3 ⋅ (x4)1/6]-3

=  [x2/3 ⋅ x2/3]-3

=  (x4/3)-3

=  x-4

=  1/x4

Example 3 :

Evaluate :

(3√x⋅ √x5) / √(25x16)

Solution :

=  (3√x⋅ √x5) / √(25x16)

=  [(x4)1/3 ⋅ (x5)1/2] / (25x16)1/2

=  (x4/3 ⋅ x5/2) / (5x8)

=  (x4/3 + 5/2 - 8) / 5

=  (x8/6 + 15/6 - 48/6) / 5

=  (x-25/6) / 5

=  1 / (5x25/6)

Example 4 :

Evaluate :

√(8x3)√(18x)

Solution :

=  √(8x⋅ 18x)

=  √(144x4)

=  (144x4)1/2

=  12x2

Example 5 :

Evaluate :

(2161/3 ⋅ 61/3)3/2

Solution :

=  [(63)1/3 ⋅ 61/3]3/2

=  (6 ⋅ 61/3)3/2

=  (61 + 1/3)3/2

=  (63/3 + 1/3)3/2

=  (64/3)3/2

=  62

=  36

Example 6 :

Evaluate :

3√(8x3⋅ 4√(625x8)

Solution :

=  (8x3)1/3 ⋅ (625x8)1/4

=  (8x3)1/3 ⋅ (625x8)1/4

=  (23)1/3(x3)1/3 ⋅ (54)1/4(x8)1/4

=  2x 5x2

=  10x1 + 2

=  10x3

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