How do you simplify #(-3ab^3)^4#?

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Answer 1 · 2017-10-24T20:35:35

See a solution process below:

We can first rewrite the expression using this rule of exponents:

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

#(-3^color(red)(1)a^color(red)(1)b^3)^4#

Now, we can use this rule to eliminate the outer exponent:

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

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

#-3^(color(red)(1)xxcolor(blue)(4))a^(color(red)(1)xxcolor(blue)(4))b^(color(red)(3)xxcolor(blue)(4)) =>#

#-3^4a^4b^12 =>#

#81a^4b^12#