How do you combine like terms in #(- 11m ^ { 4} ) ( - 6m ^ { 3} p ^ { 2} ) ^ { 2}#?

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Answer 1 · 2017-03-05T12:40:30

See the entire solution process below:

First, expand the terms in the right parenthesis by using these two rules for exponents:

#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(-11m^4)(-6m^3p^2)^2 = (-11m^4)(-6^color(red)(1)m^color(red)(3)p^color(red)(2))^color(blue)(2)#

#(-11m^4)(-6^(color(red)(1)xxcolor(blue)(2))m^(color(red)(3)xxcolor(blue)(2))p^(color(red)(2)xxcolor(blue)(2))) = (-11m^4)(-6^2m^6p^4) =#

#(-11m^4)(36m^6p^4)#

Next, rewrite the expression as:

#(-11 xx 36)(m^4m^6)p^4 = -396m^4m^6p^4#

Now, use this rule of exponents to complete the problem:

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

#-396m^color(red)(4)m^color(blue)(6)p^4 = -396m^(color(red)(4) + color(blue)(6))p^4 = -396m^10p^4#