How do you multiply #5x ^ { 3} \cdot 5y ^ { 6} y ^ { - 4} w x ^ { - 3} \cdot 3w ^ { 5}#?

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Answer 1 · 2017-04-04T20:45:15

#75y^2w^6#

#5x^3*5y^6y^-4wx^-3*3w^5#

collect like terms:

#5x^3*5y^6y^-4wx^-3*3w^5 = 5x^(3-3)*5y^(6-4)*3w^(5+1)#

laws of indices:

#a^m*a^n=a^(m+n)#

#a^m/a^n = a^(m-n)#

#x^0# (when #x!=0)##=1#

using this:
#5x^3*5y^6y^-4wx^-3*3w^5=5x^(3-3)*5y^(6-4)*3w^(5+1)=5*cancel(x^0)*5*y^2*3*w^6#

#=75y^2w^6#