Question

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

Answer 1

Given expression: $(2x^2)(3x^3)(4x)^2.$

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

Let us simplify $(4x)^2 = 4^2x^2 = 16x^2$

Therefore,  $(2x^2)(3x^3)(4x)^2=(2x^2)(3x^3)(16x^2).$

$(2x^2)(3x^3)(16x^2)=2 \times 3 \times 16 \times (x^2 \times x^3 \times x^2).$

=$96x^{2+3+2}$

$96x^{7}$.

Therefore, $(2x^2)(3x^3)(4x)^2$ is equivalent to $96x^{7}.$

Answer 2

The answer is:  " 96 x⁷ " .
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Explanation:
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Let us assume that the question asks to simplify the following:
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            →   "  (2x²) (3x³) (4x)²  "   ;  
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Note that there is only ONE variable, which is "x" .
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            →   The expression is the same as:
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            →     "  (2x²)  *  (3x³)  *  (4x)²  " ;
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→ {In other words:  Note that "multiplication" of the terms is " implied ".}. 
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Consider the following "multiplicand" :      →   "  (4x)²  " ;
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Note that:    " (4x)²  =  (4²) * (x²)  =  16x² "  ; 

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

Alternately:  " (4x)²  =  (4x) * (4x) = (4 * 4 * x * x)  =  16x² " ; 
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Now, rewrite the original expression; substituting:

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

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

                   =    " 96 *  (x²) * (x³) * (x²) " ; 
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→   Consider the following part of the expression:

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

      →  " (xª)  *  (xᵇ)  =  x⁽ª ⁺ ᵇ ⁾  "  ; 
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As such:
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     →  " (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 " . 
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The answer is:  "  96 x⁷  "  .
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      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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