What is #b^4(1/3b^2)(12b^-8)#?

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Answer 1 · 2018-04-27T12:28:52

See a solution process below:

First, rewrite the expression as:

#(1/3 * 12)(b^4 * b^2 * b^-8) =>#

#12/3(b^4 * b^2 * b^-8) =>#

#4(b^4 * b^2 * b^-8)#

Next, use this rule for exponents to multiply the #b# terms:

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

#4(b^color(red)(4) * b^color(blue)(2) * b^color(green)(-8)) =>#

#4b^(color(red)(4)+color(blue)(2)+(color(green)(-8))) =>#

#4b^(6+(color(green)(-8))) =>#

#4b^(6-color(green)(8)) =>#

#4b^-2#

Now, use this rule for exponents to eliminate the negative exponent:

#x^color(red)(a) = 1/x^color(red)(-a)#

#4b^color(red)(-2) =>#

#4/b^-color(red)(-2) =>#

#4/b^2#