How do you simplify #\frac { c ^ { - 3} } { c ^ { - 6} }#?

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Answer 1 · 2017-03-16T04:49:27

#c^(-3)/c^(-6)=c^3#

A negative exponent such as say in #a^(-m)# is interpreted as #1/a^m#.

as such #c^(-3)/c^(-6)=(1/c^3)/(1/c^6)#

i.e. #1/c^3# divided by #1/c^6#.

But as division by a fraction such as #a/b# is equivalent to multiplication by its reciprocal or multiplicative inverse #b/a#

#(1/c^3)/(1/c^6)=1/c^3xxc^6/1#

= #(cxxcxxcxxcxxcxxc)/(cxxcxxc)#

= #(cxxcxxcxxcancelcxxcancelcxxcancelc)/(cancelcxxcancelcxxcancelc)#

= #cxxcxxc#

= #c^3#