Algebra 1 help please :[ URGENT?

Question

1 simplify

( 4x^5y^2 )^2 
  ---------- 
( -2x^3y^2 ) 

Assume the denominator is not equal to zero 

2. simplify. 

(-6x^2y^3)^2 
------------- 
(3xy^2)^3 

Assume denominator is not equal to zero 


Thank you, please help!

Answer 1

• 1). The expression is  ( 4x⁵y² )²
                                       ---------- .
                                      ( -2x³y²)

Apply product rule of exponents : (ab)^m = a^m * b^m.

  ( - 16[(x⁵)² * (y²)² ])
= --------------------
       ( 2x³y²)

Apply power rule of exponents : (a^m )ⁿ = a^mn.

 ( - 8x¹⁰y⁴ )
= ----------
    ( x³y²)

=  - 8x⁷y² .

Therefore,  ( 4x⁵y² )²
                   ----------  = - 8x⁷y² .
                  ( -2x³y²)

Answer 2

Contd.........

• 2). The expression is ( - 6x²y³ )²

                                       ---------- .
                                       ( 3xy²)³

Apply product rule of exponents : (ab)^m = a^m * b^m.

  ( 36[(x²)² * (y³)² ])
= --------------------
       27x³(y²)³

Apply power rule of exponents : (a^m )ⁿ = a^mn.

   4x⁴y⁶
= -------
   3x³y⁶

= (4/3)x

= 4x/3.

Therefore,  ( - 6x²y³ )²
                      ----------  = 4x/3 .

                     ( 3xy²)³