How do you combine like terms in #(6c ^ { 3} ) ^ { 4} * 5c ^ { 5} + \frac { c ^ { 21} } { c ^ { 4} }#?

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Answer 1 · 2017-03-04T08:17:01

#6481c^17#

#(6c^3)^4*5c^5+c^21/c^4#

#:.=(6^color(red)4*c^color(red)(3 xx 4)*5c^color(red)5)+c^color(red)(21-4)#

#:.=(6^color(red)4*c^color(red)(12)*5c^color(red)5)+c^color(red)17#

#:.=(6*6*6*6*5c^color(red)12c^color(red)5)+c^color(red)(17)#

#:.=6480c^color(red)17+c^color(red)17color(red)#

#:.=c^color(red)17(6480+1)#

#:.=6481c^color(red)17#

Answer 2 · 2017-03-04T08:24:34

#= 6481c^17#

In tackling this question we will use three rules of indices:

(i) #a^mxxa^n = a^(m+n)#

(ii) # (a^m)^n = a^(mxxn)#

(iii) #1/a^m = a^-m#

Expression #= (6c^3)^4 * 5c^5 + c^21/c^4#

Apply rule (iii):

#= (6c^3)^4 * 5c^5 + c^(21-4)#

Apply rule (ii):

#= 6^4 * c^12 * 5*c^5 + c^17#

#= 1296*5 * c^12*c^5 + c^17#

Apply rule (i):

#=6480* c^(12+5) + c^17#

#=6480*c^17 +c^17#

#=c^17 (6480+1)#

#= 6481c^17#

[Also remember, "Rule (iv)": Never fear scary looking problems! :-)]