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(((2mc^(2))/(6b)))/(((10c^(4))/(3b^(3)))) Which expression is equivalent to the given quotient for all b > 0 and c > 0 ? Choose 1 answer: (A) (m)/( 10) (B) (mb^(2))/(10c^(2)) (C) (5mc^(2))/(16b^(2)) (D) (10 mc^(6))/(9b^(4))

(2mc26b)(10c43b3) \frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)} \newlineWhich expression is equivalent to the given quotient for all b>0 and c>0 ?\newlineChoose 11 answer:\newline(A) m10 \frac{m}{10} \newline(B) mb210c2 \frac{m b^{2}}{10 c^{2}} \newline(C) 5mc216b2 \frac{5 m c^{2}}{16 b^{2}} \newline(D) 10mc69b4 \frac{10 m c^{6}}{9 b^{4}}

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Q. (2mc26b)(10c43b3) \frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)} \newlineWhich expression is equivalent to the given quotient for all b>0 b>0 and c>0 c>0 ?\newlineChoose 11 answer:\newline(A) m10 \frac{m}{10} \newline(B) mb210c2 \frac{m b^{2}}{10 c^{2}} \newline(C) 5mc216b2 \frac{5 m c^{2}}{16 b^{2}} \newline(D) 10mc69b4 \frac{10 m c^{6}}{9 b^{4}}
  1. Write and simplify expression: Write down the given expression and simplify it by dividing the numerators and denominators separately.\newlineGiven expression: 2mc26b10c43b3\frac{\frac{2mc^2}{6b}}{\frac{10c^4}{3b^3}}\newlineSimplify the expression by dividing the numerators and denominators: 2mc26b×3b310c4\frac{2mc^2}{6b} \times \frac{3b^3}{10c^4}
  2. Cancel common factors: Cancel out the common factors in the numerator and the denominator.\newlineSimplify the expression: 2mc2×3b36b×10c4\frac{2mc^2 \times 3b^3}{6b \times 10c^4}\newlineCancel out the common factors: 2×3mc2b36×10bc4\frac{2 \times 3mc^2b^3}{6 \times 10bc^4}
  3. Perform cancellation: Perform the cancellation.\newline2×3mc2b36×10bc4=mc2b310bc4\frac{2 \times 3mc^2b^3}{6 \times 10bc^4} = \frac{mc^2b^3}{10bc^4}\newlineNow cancel out the common terms: c2c^2 cancels with c4c^4 leaving c2c^2 in the denominator, and bb cancels with b3b^3 leaving b2b^2 in the numerator.\newlinemc2b310bc4=mb210c2\frac{mc^2b^3}{10bc^4} = \frac{mb^2}{10c^2}
  4. Check final expression: Check the final expression against the given options.\newlineThe final simplified expression is mb210c2\frac{mb^2}{10c^2}.\newlineThis matches with option (B).

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