Question

What is 6 to the negative 1 times (-2) to the third power times (-4) to the negative 2

Answer 1

The answer is:  $\frac{1}{12}$  .
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Explanation:
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We have:   " 6⁻¹  *  (-2)³  * (-4)⁻² = ? " ;
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Note:  "6⁻¹ = $\frac{1}{6^1}$ = $\frac{1}{6}$ "  .
 
Note the following property of exponents:
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           a⁻ˣ = $\frac{1}{x^a}$ ;  {x ≠ 0}.
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Note:  (-2)³  = (-2)*(-2)*(-2) = 4*(-2) = -8 .
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Note:  (-4)⁻²  = $\frac{1}{(-4)^2}$  ;
 
                     = $\frac{1}{(-4)*(-4)}$ ;

                     = $\frac{1}{16}$ ;
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So; we have:
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6⁻¹  *  (-2)³  * (-4)⁻²  ;

=  $\frac{(1*8*1)}{(6*16)}$ ;

→ Cancel out the "8" in the "numerator" (to a "1") ; and the "16" in the number (and change to a "2"); since: {"16÷8 = 2" ; and since:  "{8÷8=1"} ;

→and we have:

$\frac{(1*1*1)}{(6*2)}$ ;

 =  $\frac{1}{12}$ .
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 → The answer is:  $\frac{1}{12}$  .
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