The answer is: [tex] \frac{1}{12} [/tex] .
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Explanation:
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We have: " 6⁻¹ * (-2)³ * (-4)⁻² = ? " ;
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Note: "6⁻¹ = [tex] \frac{1}{6^1} [/tex] = [tex] \frac{1}{6}[/tex] " .
Note the following property of exponents:
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a⁻ˣ = [tex] \frac{1}{x^a} [/tex] ; {x ≠ 0}.
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Note: (-2)³ = (-2)*(-2)*(-2) = 4*(-2) = -8 .
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Note: (-4)⁻² = [tex] \frac{1}{(-4)^2} [/tex] ;
= [tex] \frac{1}{(-4)*(-4)} [/tex] ;
= [tex] \frac{1}{16} [/tex] ;
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So; we have:
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6⁻¹ * (-2)³ * (-4)⁻² ;
= [tex] \frac{(1*8*1)}{(6*16)} [/tex] ;
→ 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:
[tex] \frac{(1*1*1)}{(6*2)} [/tex] ;
= [tex] \frac{1}{12} [/tex] .
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→ The answer is: [tex] \frac{1}{12} [/tex] .
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