How do you multiply #2u ^ { 5} \cdot 3w ^ { 2} u ^ { 8} \cdot 7w#?

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Answer 1 · 2017-06-22T00:59:47

See a solution process below:

First, rewrite the expression as:

#(2 * 3 * 7)(u^5 * u^8)(w^2 * w) => 42(u^5 * u^8)(w^2 * w)#

To simplify the #u# term use this rule for exponents:

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

#42(u^color(red)(5) * u^color(blue)(8))(w^2 * w) => 42(u^(color(red)(5)+color(blue)(8)))(w^2 * w) => 42u^13(w^2 * w)#

To multiply the #w# terms use these two rules of exponents:

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

#42u^13(w^2 * w) => 42u^13(w^color(red)(2) * w^color(blue)(1)) => 42u^13w^(color(red)(2)+color(blue)(1)) => 42u^13w^3#