How do you simplify #2x \cdot \frac { 3x ^ { 2} } { x^ - 6}#?

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Answer 1 · 2017-11-28T03:33:52

See a solution process below:

First, use this rule for exponents to simplify the fraction on the right:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#2x * (3x^color(red)(2))/x^color(blue)(-6) => 2x * 3x^(color(red)(2)-color(blue)(-6)) => 2x * 3x^(color(red)(2)+color(blue)(6)) => 2x *3x^8#

Next, rewrite this expression as:

#(2 * 3)(x * x^8) => 6(x * x^8)#

Now, use these rules for exponents to complete the simplification:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#6(x * x^8) => 6(x^color(red)(1) xx x^color(blue)(8)) => 6x^(color(red)(1) + color(blue)(8)) => 6x^9#