Given:

The expression 28x9y5 .

Definition used:

Radicals: If n is an even natural number and a>0 , or n is an odd natural number, then a1/n=an .

Property used:

1. For all real numbers a and natural number n such that an is real number, (an)n=a .

3. For all real numbers a and b and natural numbers m and n such that an and bn are real numbers, an⋅bn=abn .

Calculation:

Simplify the terms,

28x9y5=(4⋅7)(x8⋅x)(y4⋅y)  [By Property 3]=(4)(x8)(y4)⋅(7⋅x⋅y)=(4)(x8)(y4)⋅(7xy)=(4)(x8)(y4)⋅(7xy)

By the definition of radicals,

28x9y5=((4)(x8)(y4))1/2⋅7xy

Further simplify the terms of the expression as follows,

28x9y5=(4)1/2(x8)1/2(y4)1/2⋅7xy      [By Property 1]=(22)1/2(x8)1/2(y4)1/2⋅7xy =(2(2)(1/2))(x(8)(1/2))(y(4)(1/2))⋅7xy =2x4y27xy

Therefore, the simplified form of the expression 28x9y5 is 2x4y27xy .