How do you simplify #2a^2(4a^-2b^3)^-3# and write it using only positive exponents?

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Answer 1 · 2017-01-26T13:36:45

See the entire simplification process below:

First, expand the term in parenthesis using this rule for exponents:

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

#2a^2(4a^-2b^3)^-3 -> 2a^2(4^-3a^(-2xx-3)b^(3xx-3)) -> 2a^2(4^-3a^6b^-9)#

Now, group like terms:

#(2xx4^-3)(a^2 xx a^6)b^-9#

Then, combine like terms using this rule of exponents:

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

Giving:

#2a^(2+6)4^-3b^-9 -> 2a^8 4^-3b^-9#

Now, use this rule of exponents to remove the negative exponents:

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

Giving:

#(2a^8)/(4^(- -3)b^(- -9)) -> (2a^8)/(4^3b^9) -> (2a^8)/(64b^9) ->#

#a^8/(32b^9)#