How do you multiply #(5a ^ { 3} b ) ^ { 2} \cdot ( 2a ^ { 3} b ^ { 4} )#?

1 Answer
Mia
Mar 23, 2017

#=50a^9b^6#

Explanation:

In this exercise we have to use some properties of powers:
#" "#
#color(green)((axxb)^n=a^nxxb^n#
#" "#
Power of a power
#" "#
#color(blue)((a^m)^n=a^(mxxn)#
#" "#
Multiplication of powers with same base:
#" "#
#color(red)(a^bxxa^c=a^(b+c)#
#" "#
#(5a^3b)^2.(2a^3b^4)#
#" "#
#=color(green)(5^2xx(a^3)^2xxb^2).2xxa^3xxb^4#
#" "#
#=25xxcolor(blue)(a^(3xx2))xxb^2xx2xxa^3xxb^4#
#" "#
#=25xxcolor(blue)(a^6)xxb^2xx2xxa^3xxb^4#
#" "#
#=25xx2xxa^6xxa^3xxb^2xxb^4#
#" "#
#=50xxcolor(red)(a^(6+3))xxcolor(red)(b^(2+4))#
#" "#
#=50xxcolor(red)(a^9)xxcolor(red)(b^6)#
#" "#
#=50a^9b^6#

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