How to simplifiy?

Question

(3x^5y^3)^3 (5xy^7)^2

question got me confused because it askdd simplifiy so there are no negative exponents.

Answer 1

(3x⁵y³)³ (5xy⁷)²

 

     = 3³(x⁵)³(y³)³(5)²*(x)²(y⁷)²

 

     = 27x¹⁵y⁹25x²y¹⁴

 

     = (27*25)(x¹⁵⁺²)(y⁹⁺¹⁴)

 

     = 675x¹⁷y²³

Answer 2

Dear Youssef,

    Let me give you two other examples that will show you the procedures to answering this problem.

 

Here is the rule first: Multiply every power by the outside power. There are two examples below:

 

  (5²ab²)⁹=   5^2*9 a^1*9 b^2*9= 5¹⁸a⁹b¹⁸

 

(2X⁴Y¹⁰)² (4XY⁵)³ = [2²X^4*2 Y^10*2 ]*[4^(1*3)X ^(1*3)Y^(5*3)]=[4X⁸ Y²⁰] ^[64X³Y¹⁵]=256 X¹¹Y³⁵

 

Once I got everything simplified, I just added the powers:  a * a²= a ⁽¹⁺²⁾ =a³

 

I hope that I helped you. Please give me a thumbs up if I did.

 

                                                                                   Susan C.