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lara31 [8.8K]
2 years ago
15

.

Mathematics
1 answer:
olchik [2.2K]2 years ago
5 0
The correct answer is:  [B]:  " 25 a²⁵ b²⁵ " .
_________________________________________________________
<span>Explanation:
_________________________________________________________
Given the expression: 
_________________________________________________________
       </span>→  " (−5a⁵b⁵)² (a³b³)⁵  " ;   Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
       →    "(−5a⁵b⁵)² " . 

→  "(−5a⁵b⁵)²  = (-5)² * (a⁵)² * (b⁵)²  = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾  = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;

{Note the following properties of exponents:
    (xy)ⁿ = xⁿ * yⁿ ; 

    (xᵃ)ᵇ = x⁽ᵃ * ᵇ) ; 

    (xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________

Then, we examine:
______________________________________
      →    "(a³b³)⁵ " .

→  "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________

So:   " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾  " ; 
________________________________________
Now, we simplify:

          →  " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ; 

→  " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;
 
               =  25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾  ;

               =  25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;

               =  25a⁽²⁵⁾ b⁽²⁵⁾ ; 
_______________________________________________
  →  which is:  Answer choice:  [B]:  " 25 a²⁵ b²⁵ " .
______________________________________________
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