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

1 Answer
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.