How do you evaluate #\frac { m ^ { 7} \cdot m ^ { - 50} } { m ^ { - 19} \cdot m ^ { 5} }#?

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Answer 1 · 2017-12-06T03:07:32

See a solution process below:

First, use this rule of exponents to simplify the numerator and the denominator:

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

#(m^color(red)(7) * m^color(blue)(-50))/(m^color(red)(-19) * m^color(blue)(5)) =>#

#m^(color(red)(7)+color(blue)(-50))/m^(color(red)(-19)+color(blue)(5)) =>#

#m^-43/m^-14#

Now, use this rule of exponents to complete the evaluation:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#m^color(red)(-43)/m^color(blue)(-14) =>#

#1/m^(color(blue)(-14)-color(red)(-43)) =>#

#1/m^(color(blue)(-14)+color(red)(43)) =>#

#1/m^29#