Explain these problems please!!?

Question

I'm soo confused!!! :
1. 5a^-3b^4/15cd^-2

2. 8x^-2y^4z^-3

Answer 1

1. 5a^-3b^4/15cd^-2

( 5a^-3 b⁴ ) / ( 15cd^-2 )                                      (a^-1=1/a)

So , ( 5 ( 1/a³ ) b⁴ ) / ( 15c(1/d²) )

Simplfy    

( 5b⁴ / a³) / ( 15c / d²)                                 ( a/b ) / ( c/d )= ( ad / bc )

( 5b⁴ / a³) * ( d²/15c )

( 5 b⁴ d² ) / ( 15c a³)

There fore   ( 5 b⁴ d² ) / ( 15c a³)

Comments

5b⁴ d² / 15c a³

= b⁴ d² / 3c a³

Answer 2

2. 8x^-2y^4z^-3

= 8x^-2y⁴z^-3                               (a^-1=1/a)

= 8( 1/x² )y⁴ ( 1 / z³ )

Simplfy  

= 8 y⁴ ( 1 / x²z³)

Simplfy 

=( 8 y⁴ / x² z³ )

 there fore ( 8 y⁴ / x² z³ )

Answer 3

1. 5a^-3b^4/15cd^-2

( 5a^-3 b⁴ ) / ( 15cd^-2 )                                      (a^-1=1/a)

So , ( 5 ( 1/a³ ) b⁴ ) / ( 15c(1/d²) )

Simplfy    

( 5b⁴ / a³) / ( 15c / d²)                                 ( a/b ) / ( c/d )= ( ad / bc )

( 5b⁴ / a³) * ( d²/15c )

( 5 b⁴ d² ) / ( 15c a³)

(b^4d^2) / 3ca^3

There fore  b^4d^2) / 3ca^3

 

Answer 4

1. 5a^-3b^4/15cd^-2

( 5a^-3 b⁴ ) / ( 15cd^-2 )                                      (a^-1=1/a)

So , ( 5 ( 1/a³ ) b⁴ ) / ( 15c(1/d²) )

Simplfy    

( 5b⁴ / a³) / ( 15c / d²)                                 ( a/b ) / ( c/d )= ( ad / bc )

( 5b⁴ / a³) * ( d²/15c )

( 5 b⁴ d² ) / ( 15c a³)

Simplfy

( b⁴ d² ) / ( 3 c a³)

There fore

( 5a^-3 b⁴ ) / ( 15cd^-2 ) = ( b⁴ d² ) / ( 3 c a³)