How do you multiply #(- 2a ^ { - 2} ) ^ { 3} ( - 5a ^ { - 3} ) ^ { 2}#?

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Answer 1 · 2018-03-24T10:50:05

See a solution process below:

First, eliminate the out exponents by using this rule for exponents:

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

#(-2a^color(red)(-2))^color(blue)(3)(-5a^color(red)(-3))^color(blue)(2) =>#

#(-2^3a^(color(red)(-2) xx color(blue)(3)))(-5^2a^(color(red)(-3) xx color(blue)(2))) =>#

#(-8a^color(red)(-6))(25a^color(blue)(-6)) =>#

#(-8 xx 25)(a^color(red)(-6) xx a^color(blue)(-6)) =>#

#-200(a^color(red)(-6) xx a^color(blue)(-6))#

Next, 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))#

#-200a^(color(red)(-6)+color(blue)(-6)) =>#

#-200a^color(red)(-12)#

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

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

#(-200)/a^color(red)(- -12) =>#

#-200/a^color(red)(12)#