How do you simplify #\frac { 5x ^ { 6} y ^ { 7} z } { 15x ^ { 2} y ^ { 5} z }#?

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Answer 1 · 2017-05-21T18:56:42

#=(x^4y^2)/3#

Divide or simplify the coefficients as normal.

Subtract the indices of like bases.

#(5x^6y^7z)/(15x^2y^5z#

#=(cancel5color(blue)(x^6)color(magenta)(y^7)cancelz)/(cancel15_3color(blue)(x^2)color(magenta)(y^5)cancelz#

#=(color(blue)(x^(6-2))color(magenta)(y^(7-5)))/3#

#=(x^4y^2)/3#

Answer 2 · 2017-05-21T19:34:28

#frac(x^(4) y^(2))(3)#

We have: #frac(5 x^(6) y^(7) z)(15 x^(2) y^(5) z)#

Using the laws of exponents:

#= frac(5)(15) cdot x^(6 - 2) cdot y^(7 - 5) cdot z^(1 - 1)#

#= frac(1)(3) cdot x^(4) cdot y^(2) cdot z^(0)#

#= frac(1)(3) cdot x^(4) cdot y^(2) cdot 1#

#= frac(x^(4) y^(2))(3)#