Question

Which expression is the simplest form of..

Answer 1

Answer:   Answer choice:  [A]:  " x⁻ ⁴ " .

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Step-by-step explanation:

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Given:

{x ^ $^( {\frac{-4}{7}) }^7$ ;

 →  Simplify.

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Note the following property of exponents:

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 →   (xᵃ) ᵇ  =  x ⁽ ᵃ * ᵇ ⁾   ;    {a ≠ 0 ;  b ≠ 0 .} .

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As such:

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→    {x ^ $^( {\frac{-4}{7}) }^7$  ;  

       =  x ^ ($[(\frac{-4}{7}) * 7 ]$  ;

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Find:  $[(\frac{-4}{7}) * 7 ] ; Note: " 7 = [tex]\frac{7}{1}$ " .

So:  Find:  " $[(\frac{-4}{7} * [tex]\frac{7}{1}$ " ;

The 2 (two) "7 's " ;  cancel out to "1" ;  

      →   {since:  " 7 ÷ 7 = 1 " } ;

And we have:

  -4 * 1 = -4 .

So, we have:

       " x ⁻ ⁴ "  ; which is:  Answer choice:  [A]:  " x⁻ ⁴  " .

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Choice:  [C} —  is also an equivalent;  however, the question asks for the "simplest form" — which is:  Answer choice:  [A].

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