How do you simplify #\frac{y^{6}}{8y+72}\times \frac{9y+81}{9y^{9}}#?

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Answer 1 · 2017-10-21T02:57:28

#=>1/(8y^3)#

#\frac{y^{6}}{8y+72}\times \frac{9y+81}{9y^{9}}#

Multiply:

#=>\frac{y^{6}(9y+81)}{(8y+72)9y^{9}}#

Take 9 common outside the bracket:

#=>\frac{9y^{6}(y+9)}{8(y+9)9y^{9}}#

Deduce:

#=>frac{cancel9y^{6}cancel((y+9))}{8cancel((y+9))cancel9y^{9}}#

#=>frac{y^{6}}{8y^{9}}#

Rule of indices: #a^m/a^n = a^(m-n)#

#=> (y^(6-9))/ 8#

#=>y^-3/8#
Or

#=>1/(8y^3)#