Which expression is equivalent to (2x2)(3x3)(4x)2?

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  " 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!

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