(((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))

Write and simplify expression: Write down the given expression and simplify it by dividing the numerators and denominators separately. Given expression: $\frac{\frac{2mc^2}{6b}}{\frac{10c^4}{3b^3}}$ Simplify the expression by dividing the numerators and denominators: $\frac{2mc^2}{6b} \times \frac{3b^3}{10c^4}$Cancel common factors: Cancel out the common factors in the numerator and the denominator. Simplify the expression: $\frac{2mc^2 \times 3b^3}{6b \times 10c^4}$ Cancel out the common factors: $\frac{2 \times 3mc^2b^3}{6 \times 10bc^4}$Perform cancellation: Perform the cancellation. $\frac{2 \times 3mc^2b^3}{6 \times 10bc^4} = \frac{mc^2b^3}{10bc^4}$ Now cancel out the common terms: $c^2$ cancels with $c^4$ leaving $c^2$ in the denominator, and $b$ cancels with $b^3$ leaving $b^2$ in the numerator. $\frac{mc^2b^3}{10bc^4} = \frac{mb^2}{10c^2}$Check final expression: Check the final expression against the given options. The final simplified expression is $\frac{mb^2}{10c^2}$. This matches with option (B).

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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))

$\frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)}$ $\newline$ Which expression is equivalent to the given quotient for all b>0 and c>0 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{m}{10}$ $\newline$ (B) $\frac{m b^{2}}{10 c^{2}}$ $\newline$ (C) $\frac{5 m c^{2}}{16 b^{2}}$ $\newline$ (D) $\frac{10 m c^{6}}{9 b^{4}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

\frac{\left(\frac{2 m c^{2}}{6 b}\right)}{\left(\frac{10 c^{4}}{3 b^{3}}\right)}

\newline

Which expression is equivalent to the given quotient for all

b>0

and

c>0

\newline

Choose

1

answer:

\newline

(A)

\frac{m}{10}

\newline

(B)

\frac{m b^{2}}{10 c^{2}}

\newline

(C)

\frac{5 m c^{2}}{16 b^{2}}

\newline

(D)

\frac{10 m c^{6}}{9 b^{4}}

Write and simplify expression: Write down the given expression and simplify it by dividing the numerators and denominators separately. $\newline$ Given expression: $\frac{\frac{2mc^2}{6b}}{\frac{10c^4}{3b^3}}$ $\newline$ Simplify the expression by dividing the numerators and denominators: $\frac{2mc^2}{6b} \times \frac{3b^3}{10c^4}$
Cancel common factors: Cancel out the common factors in the numerator and the denominator. $\newline$ Simplify the expression: $\frac{2mc^2 \times 3b^3}{6b \times 10c^4}$ $\newline$ Cancel out the common factors: $\frac{2 \times 3mc^2b^3}{6 \times 10bc^4}$
Perform cancellation: Perform the cancellation. $\newline$ $\frac{2 \times 3mc^2b^3}{6 \times 10bc^4} = \frac{mc^2b^3}{10bc^4}$ $\newline$ Now cancel out the common terms: $c^2$ cancels with $c^4$ leaving $c^2$ in the denominator, and $b$ cancels with $b^3$ leaving $b^2$ in the numerator. $\newline$ $\frac{mc^2b^3}{10bc^4} = \frac{mb^2}{10c^2}$
Check final expression: Check the final expression against the given options. $\newline$ The final simplified expression is $\frac{mb^2}{10c^2}$ . $\newline$ This matches with option (B).