Question

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

Answer 1

The answer is: " 96 x⁷ " .
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Step-by-step 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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Answer 2

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 * 3 * 16 * (x^2 * x^3 * x^2).`

=
`96x^(2+3+2)`

`96x^(7)`.

Therefore,
`(2x^2)(3x^3)(4x)^2` is equivalent to
`96x^(7).`