How do you simplify #\frac { b ^ { 95} c ^ { - 4} } { b ^ { 58} c \cdot b ^ { - 8} c ^ { - 1} }#?

1 Answer
AA_123
Apr 17, 2017

#b^45/c^4#

Explanation:

First of all simplify the numerator and the denominator by multiplying numbers with same base (i.e. #c# with #c# and #b# with #b#). (Remember, when you are multiplying you are adding the exponents, and when you are dividing you are subtracting them).

#(b^95c^-4)/(b^58color(magenta)cb^-8c^-1)#

This #color(magenta)c# is the same as #c^1#

#(b^95c^-4)/(b^color(red)58b^color(green)(-8)c^-1c^color(blue)1)#

#(b^95c^-4)/((b^(color(red)58color(green)(-8)))(c^(-1+color(blue)1)))#

#=(b^95c^-4)/(b^50c^0)#

Anything to the power of #0# is one, so it can be removed

#=(b^color(red)95c^-4)/b^color(red)50#

Subtract the smaller exponent from the same base

#=(b^(color(red)95-50)c^-4)/b^(color(red)50-50)#

#=(b^45c^-4)/b^0#

#=b^45c^-4#

The definition of negative exponents is #a^-m=1/a^m# so,

#b^45c^-4=b^45*1/c^4=color(purple)(b^45/c^4)#

This is the final answer, note that when you simplify expressions with negative exponents you need to remove them and convert them to a positive exponents.

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