" " .
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Step-by-step explanation:
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We are asked to simplify the following given expression:
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;
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Let us start with the "numerator" ; which functions as a separate "fraction"—in and of itself—with its own numerator and denominator:
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;
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Note the following "division" property of exponents:
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→ ; .
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Then:
→ (\frac{2b^3c}{a^3b^2c^2})^4 ;
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= ; ; ; .
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Then, start by simplifying "this particular numerator":
→ ;
Note the following "multiplication" property of exponents:
→ ; .
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Then:
→ ;
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The continue by simplifying "this particular denominator":
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→
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And we have:
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→ .
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Note the following properties of exponents:
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→ ; .
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→ ; .
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So, we have:
→ \frac{16b^1^2c^4}{a^1^2b^8c^8} ;
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→ 16 ÷ 1 = 16 ; ("1" is the "implied coefficient") ; in the numerator.
→ ; stays in the denominator;
→ ; replaces the original: " " [in the numerator]; is eliminated in the denominator;
→ ; The original " " [in the numerator] is eliminated; the original " " [in the denominator] is replaced with " " . ________________
And the expression is rewritten as:
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→ ;
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→ Now, from the original given problem, we divide this value by "6" ;
which is the same value we get by multiplying this value by: " " ;
→ as follows:
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→ ;
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Considering the "16" and the "6" ; each of these can be divided by "2" ;
Specifically, " (16 ÷2 = 8) " ; and: " (6 ÷ 2 = 3) " .
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So, we can rewrite the expression — by substituting "8" in lieu of the "16" ; and "3" in lieu of the "6" ; as follows:
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→ ;
And further simplify;
→
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Hope this helps!
Best wishes!
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