# Evaluate: (3a^3c^n)/(7x^3b^n) * (49x^{n-1}b^{n+2})/(9a^{n+5)c^{n+1}}/(c)/(a^2x^4)

## Expression: $\frac{ 3{a}^{3}{c}^{n} }{ 7{x}^{3}{b}^{n} } \times \frac{ 49{x}^{n-1}{b}^{n+2} }{ 9{a}^{n+5}{c}^{n+1} }\div\frac{ c }{ {a}^{2}{x}^{4} }$

To divide by a fraction, multiply by the reciprocal of that fraction

$\frac{ 3{a}^{3}{c}^{n} }{ 7{x}^{3}{b}^{n} } \times \frac{ 49{x}^{n-1}{b}^{n+2} }{ 9{a}^{n+5}{c}^{n+1} } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the greatest common factor $7$

$\frac{ 3{a}^{3}{c}^{n} }{ {x}^{3}{b}^{n} } \times \frac{ 7{x}^{n-1}{b}^{n+2} }{ 9{a}^{n+5}{c}^{n+1} } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the common factor ${b}^{n}$

$\frac{ 3{a}^{3}{c}^{n} }{ {x}^{3} } \times \frac{ 7{x}^{n-1}{b}^{2} }{ 9{a}^{n+5}{c}^{n+1} } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the greatest common factor $3$

$\frac{ {a}^{3}{c}^{n} }{ {x}^{3} } \times \frac{ 7{x}^{n-1}{b}^{2} }{ 3{a}^{n+5}{c}^{n+1} } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the common factor ${a}^{3}$

$\frac{ {c}^{n} }{ {x}^{3} } \times \frac{ 7{x}^{n-1}{b}^{2} }{ 3{a}^{n+2}{c}^{n+1} } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the common factor ${c}^{n}$

$\frac{ 1 }{ {x}^{3} } \times \frac{ 7{x}^{n-1}{b}^{2} }{ 3{a}^{n+2}c } \times \frac{ {a}^{2}{x}^{4} }{ c }$

Cancel out the common factor ${x}^{3}$

$\frac{ 7{x}^{n-1}{b}^{2} }{ 3{a}^{n+2}c } \times \frac{ {a}^{2}x }{ c }$

Cancel out the common factor ${a}^{2}$

$\frac{ 7{x}^{n-1}{b}^{2} }{ 3{a}^{n}c } \times \frac{ x }{ c }$

Multiply the fractions

$\frac{ 7{b}^{2}{x}^{n} }{ 3{a}^{n}{c}^{2} }$

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