Question

Simplify (4x to the power of 3) power of 2

Answer 1

Simplify (4x to the power of 3) power of 2

Explanation:

The school I go to tells me to do this:

(4x^3)^2

(4x^3)(4x^3)

(4)(4) - 16

(x^3)(x^3) - x^6 bc you add the exponents

16x^6 which is correct bc my teacher has checked us on that before in class bc we have had equations like that ^_^

Answer 2

The correct answer is: " 4096 x⁶ " .

Step-by-step explanation:

Given: [(4x)³] ² ; Simplify.

Method 1)
Note the following multiplication property of exponents:
⇒ (aᵇ)ᶜ = a⁽ᵇ*ᶜ⁾ ;

As such:

[ [(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;

Now; note the following property of exponents:
(ab)ᶜ = aᶜ * bᶜ ;

As such: (4x)⁶ = 4⁶ * x⁶ ;

Now; we can simplify 4⁶ ; by using a calculator:
→ 4⁶ = 4096 ;

Or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;

= (4 * 4) * 4 * 4 * 4 * 4 ;

= 16 * 4 * 4 * 4 * 4 * ) ;

= (16 * 4) * 4 * 4 * 4 ;

= 64 * 4 * 4 * 4 ;

= (64 * 4) * 4 * 4 ;

= (126 * 4) * 4

= (256) * 4 ;

= 4096 .
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or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;

= (4 * 4) * (4 * 4) * (4 * 4) ;

= 16 * 16 * 16 ;

= (16 * 16) * 16 ;

= (256) * 16 , = 4096.

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So: [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
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Method 2) Given: [(4x)³] ² ;

(4x)³ = 4x * 4x * 4x ;

[(4x)³]² = (4x * 4x * 4x)²

= (4x * 4x * 4x) * (4x * 4x * 4x) ;

= (4 * 4 * 4 * x * x * x * 4 * 4 * 4 * x * x * x ;

= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; (see Method 1 above).
⇒ (x * x * x * x * x * x) = x⁶ ;

⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
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Method 3)
[(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;

(4x)⁶ = 4x * 4x * 4x * 4x * 4x * 4x ;

= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

= (4 * 4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x) ;

⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; [see Method 1 above].
⇒ (x * x * x * x * x * x) = x⁶ ;

⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ .

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The correct answer is: " 4096 x⁶ " .

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Hope this is helpful.

Best wishes in your academic endeavors!
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