Respuesta :

JonHenderson55
The answer is:  " 96 x⁷ " .
________________________________________________________
Explanation:
________________________________________________________
Let us assume that the question asks to simplify the following:
________________________________________________________
 
            →   "  (2x²) (3x³) (4x)²  "   ;  
________________________________________________________
 
Note that there is only ONE variable, which is "x" .
________________________________________________________
            →   The expression is the same as:
________________________________________________________
            →     "  (2x²)  *  (3x³)  *  (4x)²  " ;
________________________________________________________

→ {In other words:  Note that "multiplication" of the terms is " implied ".}. 
________________________________________________________

Consider the following "multiplicand" :      →   "  (4x)²  " ;
________________________________________________________

Note that:    " (4x)²  =  (4²) * (x²)  =  16x² "  ; 

Alternately:  " (4x)²  =  (4 * 4) * (x²)  =  16x² "  ; 

Alternately:  " (4x)²  =  (4x) * (4x) = (4 * 4 * x * x)  =  16x² " ; 
_________________________________________________________

Now, rewrite the original expression; substituting:

           →    " 16x² " ; (in lieu of the original:  " (4x)² " ; as follows:
_________________________________________________________
 
           →   " (2x²) (3x³) (16x²) "  ;
_________________________________________________________

           →   " (2x²) (3x³) (16x²) " ; 

                  =   " 2 * 3 * 16 * (x²) * (x³) * (x²) " ; 

                   =    " 96 *  (x²) * (x³) * (x²) " ; 
_________________________________________________________

→   Consider the following part of the expression:

      →  " (x²) * (x³) * (x²) " ; 
_________________________________________________________
Note the following property of exponents:

      →  " (xª)  *  (xᵇ)  =  x⁽ª ⁺ ᵇ ⁾  "  ; 
_________________________________________________________
As such:
_________________________________________________________

     →  " (x²) * (x³) * (x²)   =   x⁽ ² ⁺ ³ ⁺ ² ⁾   =  x ⁷ "  ; 

Now, bring down the " 96 " ;  and rewrite the simplified original expression; 
   
     →  which is the answer:  " 96 x⁷ " . 
_________________________________________________________
The answer is:  "  96 x⁷  "  .
_________________________________________________________
      I hope this lengthy—yet detailed—explanation has been helpful to you.  If it has; or if you have questions, please comment below.

       Best wishes!
_________________________________________________________

Given expression: [tex](2x^2)(3x^3)(4x)^2.[/tex]

In order to simplify it to get an equivalent expression, we need to multiply all terms.

Let us simplify [tex](4x)^2 = 4^2x^2 = 16x^2[/tex]

Therefore,  [tex](2x^2)(3x^3)(4x)^2=(2x^2)(3x^3)(16x^2).[/tex]

[tex](2x^2)(3x^3)(16x^2)=2 \times 3 \times 16 \times (x^2 \times x^3 \times x^2).[/tex]

=[tex]96x^{2+3+2}[/tex]

[tex]96x^{7}[/tex].

Therefore, [tex](2x^2)(3x^3)(4x)^2[/tex] is equivalent to [tex]96x^{7}.[/tex]


Otras preguntas