What is the solution to the equation ^3sqrt m-4- ^3sqrt 2m+8=0 a. m= -24 b. m= -12 c. m= -6 d. m= -4

The correct answer is:  [B]:  " m = -12 " .  
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Explanation:
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Given the equation:

→   "  ³√(m − 4)  −  ³√(2m + 8)  =  0  " ;   Solve for "m" ; 

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We start by rewriting the terms in the equation:
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Note the following property of exponents:
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       → "  a ⁽ ˣ / ʸ⁾  =  ʸ√(aˣ)   ;  { y  0 } "  ; 
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So, rewrite:   "     ³√(m − 4) " ;  as:  "  (m − 4) ⁽ ¹/³⁾ "  ; 

and rewrite:  "    ³√(2m + 8) " ; as:  " (2m + 8) ⁽ ¹/³⁾ " ;
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And rewrite the question as:
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 →    "  (m − 4) ⁽ ¹/³⁾     −     (2m + 8) ⁽ ¹/³⁾   =   0 "  ;   Solve for "m" ; 
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Add  " (2m + 8) ¹/³ "  to EACH SIDE of the equation; as follows:
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       →   (m − 4) ¹/³⁾  −  (2m + 8)¹/³  +  (2m + 8) ¹/³  =  0 + (2m + 8) ¹/³  ;

to get: 
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    →   "  (m − 4) ¹/³   =   (2m + 8) ¹/³ "   ;  
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 →  { Note:  If   " x ⁿ  =   y ⁿ    ;   then  " x  =  y " .} . 
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    →   "  m  −  4   =  2m  +  8 " ;  Solve for "m" ; 
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Subtract "2m" from each side of the equation; & add "4" to each side of the equation; as follows:
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              m  −  4  −  2m  +  4   =  2m  +  8  −  2m  +  4  ;

to get:
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     →   -1m   =  12 ; 

Now, divide each side of the equation by "-1 " ;
     to isolation "m" on one side of the equation; & to solve for "m" ; 

    →    -1m / -1  = 12 / -1 ; 
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to get:
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" m = -12 " ;  

→  which is:  Answer choice:  [B]:  " m = -12 " .
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Hope this helps!
       Best wishes.
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