How do you simplify # (16q^0 r^-6) /( 4q^-3 r^-7)#?

1 Answer
Jan 24, 2016

Answer:

#(16q^0r^(-6))/(4q^(-3)r^(-7))=4q^3r#

with exclusions #q!=0# and #r!=0#

Explanation:

If #a != 0# and #b# and #c# are integers, then #a^b/a^c = a^(b-c)#

So:

#(16q^0r^(-6))/(4q^(-3)r^(-7))#

#=(16/4)(q^0/q^(-3))(r^(-6)/r^(-7))#

#=4 q^(0-(-3)) r^((-6)-(-7))#

#=4q^3r^1#

#=4q^3r#

with exclusions #q!=0# and #r!=0#

The exclusions are required since if #q=0# or #r=0# then at least one of #q^(-3)#, #r^(-6)#, #r^(-7)# is undefined.