How do you simplify #\frac { 6c ^ { 7} } { 3c \cdot c ^ { 2} }#?

Question

488 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-22T12:37:05

See the entire solution process below:

First, rewrite the expression as:

#(6/3)(c^7/(c * c^2)) = 2(c^7/(c * c^2))#

Next, use these rules of exponents to simplify the numerator of the remaining fraction:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#2(c^7/(c * c^2)) = 2(c^7/(c^color(red)(1) * c^color(blue)(2))) = 2(c^7/c^(color(red)(1) + color(blue)(2))) = 2(c^7/c^3)#

Now, use this rule for exponents to complete the simplification:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#2(c^color(red)(7)/c^color(blue)(3)) = 2x^(color(red)(7)-color(blue)(3)) = 2x^4#