How do you simplify #((4a³b)/(a²b³)) * ((3b²)/(2a²b^4))#?

1 Answer
Don't Memorise
Oct 11, 2015

#((4a³b)/(a²b³)) * ((3b²)/(2a²b^4)) = color(green)(6/( a *b^4)#

Explanation:

We know that #color(blue)(a^m/a^n = a^(m-n)#

First, we combine the constants and the common variables together
#((4a³b)/(a²b³)) * ((3b²)/(2a²b^4))#
# = ((4*3)/2) * (a^3/(a^2*a^2)) * ((b*b^2)/(b^3*b^4))#

We know that #color(blue)((x^m*x^n) = x^(m+n)#

#= 6 * (a^3/(a^(2+2))) * (b^(1+2)/(b^(3+4)))#

#= 6 * (a^3/(a^4)) * (b^3/(b^7))#

We also know that #color(blue)(x^m/x^n = x^(m-n)#

#= 6 * (a^(3-4)) * (b^(3-7))#

# = 6* a^-1 *b^-4#

We know that #color(blue)(x^-m = 1/x^m#

# = 6/( a *b^4)#

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