How do you multiply #3b a ^ { 4} \cdot 3b a ^ { - 1} \cdot 2b ^ { 3}#?

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Answer 1 · 2017-05-16T22:24:35

See a solution process below:

First, rewrite this expression as:

#(3 * 3 * 2)(a^4 * a^-1)(b * b * b^3) => 18(a^4 * a^-1)(b * b * b^3)#

Now, use this rule of exponents to multiply the #a# terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#18(a^color(red)(4) * a^color(blue)(-1))(b * b * b^3) => 18(a^(color(red)(4) + color(blue)(-1)))(b * b * b^3) =>#

#18a^3(b * b * b^3)#

Now, use this rule and the above rule of exponents to multiply the #b# terms:

#a = a^color(red)(1)#

#18a^3(b * b * b^3) => 18a^3(b^color(red)(1) * b^color(blue)(1) * b^color(green)(3)) => 18a^3b^(color(red)(1) + color(blue)(1) + color(green)(3)) =>#

#18a^3b^5#