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(a^(8)b^(-2))/(a^(2)b^(10)) Which of the following is equivalent to the given expression for a,b!=0 ? Choose 1 answer: (A) a^(4)b^(-5) (B) a^(6)b^(12) (C) (a^(4))/(b^(-5)) (D) (a^(6))/(b^(12))

a8b−2a2b10 \frac{a^{8} b^{-2}}{a^{2} b^{10}} \newlineWhich of the following is equivalent to the given expression for a,b≠0 a, b \neq 0 ?\newlineChoose 11 answer:\newline(A) a4b−5 a^{4} b^{-5} \newline(B) a6b12 a^{6} b^{12} \newline(C) a4b−5 \frac{a^{4}}{b^{-5}} \newline(D) a6b12 \frac{a^{6}}{b^{12}}

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Q. a8b−2a2b10 \frac{a^{8} b^{-2}}{a^{2} b^{10}} \newlineWhich of the following is equivalent to the given expression for a,b≠0 a, b \neq 0 ?\newlineChoose 11 answer:\newline(A) a4b−5 a^{4} b^{-5} \newline(B) a6b12 a^{6} b^{12} \newline(C) a4b−5 \frac{a^{4}}{b^{-5}} \newline(D) a6b12 \frac{a^{6}}{b^{12}}
  1. Given expression: We are given the expression (a8b−2)/(a2b10)(a^{8}b^{-2})/(a^{2}b^{10}). To simplify this expression, we use the properties of exponents, specifically the quotient rule which states that when dividing like bases, we subtract the exponents: am/an=am−na^{m}/a^{n} = a^{m-n} and bm/bn=bm−nb^{m}/b^{n} = b^{m-n}.
  2. Applying quotient rule: Applying the quotient rule to the given expression, we get:\newlinea8−2b−2−10=a6b−12a^{8-2}b^{-2-10} = a^{6}b^{-12}.
  3. Simplified expression: The simplified expression a6b−12a^{6}b^{-12} can be rewritten as (a6)/(b12)(a^{6})/(b^{12}) because b−12=1/b12b^{-12} = 1/b^{12}.
  4. Comparing with answer choices: Now we compare our simplified expression with the answer choices. The expression (a6)/(b12)(a^{6})/(b^{12}) matches with choice (D).

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