How do you multiply #2v ^ { 7} \cdot 3x ^ { 4} v ^ { 8} \cdot 5x#?

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Answer 1 · 2017-06-22T01:30:14

#2v^7*3x^4v^8*5x=color(blue)(30v^15x^5#

Multiply:

#2v^7*3x^4v^8*5x#

Multiply the coefficients #2#, #3#, and #5#, and insert the result back into the expression. #2xx3xx5=30#

#30v^(7)v^8x^(4)x#

Apply the exponent product rule: #a^ma^n=a^(m+n)# Reminder: a variable with no exponent is understood to have #1# as its exponent: #a=a^1#.

#30v^(7+8)x^(4+1)#

Now add the exponents for #x# and #v#.

#30v^15x^5# #lArr# Answer

Answer 2 · 2017-06-22T01:33:26

See a solution process below:

First, rewrite the expression as:

#(2 * 3 * 5)(x^4 * x)(v^7 * v^8) => 30(x^4 * x)(v^7 * v^8)#

Next, use these rules of exponents to multiply the #x# terms:

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

#30(x^4 * x)(v^7 * v^8) => 30(x^color(red)(4) * x^color(blue)(1))(v^7 * v^8) =>#

#30x^(color(red)(4)+color(blue)(1))(v^7 * v^8) => 30x^5(v^7 * v^8)#

Now, use this rule of exponents to multiply the #v# terms:

#30x^5(v^7 * v^8) => 30x^5(v^color(red)(7) * v^color(blue)(8)) => 30x^5v^(color(red)(7)+color(blue)(8)) =>#

#30x^5v^15#