How do you evaluate #3v \cdot 4x ^ { 4} \cdot 4v ^ { 7} x ^ { 6}#?

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Answer 1 · 2018-01-30T14:53:14

See a solution process below:

First, rewrite the expression as:

#(3 * 4 * 4)(x^4 * x^6)(v * v^7) =>#

#48(x^4 * x^6)(v * v^7)#

Next, use this rule for exponents to rewrite the #v# term:

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

#48(x^4 * x^6)(v^color(red)(1) * v^7)#

Now, use this rule of exponents to evaluate the #x# and #v# terms:

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

#48(x^color(red)(4) * x^color(blue)(6))(v^color(red)(1) * v^color(blue)(7)) =>#

#48x^(color(red)(4)+color(blue)(6))v^(color(red)(1)+color(blue)(7)) =>#

#48x^10v^8#