How do you multiply #(v ^ { 2} ) ^ { 3} \cdot 2v u ^ { 5}#?

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Answer 1 · 2017-05-08T20:17:16

See below.

Let's first clear the exponent from the first term.

#(v ^ { 2} ) ^ { 3} \cdot 2v u ^ { 5}#

Since it is a power raised to another power, we multiply the exponents.

#v^6\cdot 2v u ^ { 5}#

Now let's combine like-terms. Since #v^6# is only similar to #v#, and since the terms are being multiplied, we add the exponents.

#v^6\cdot 2v u ^ { 5}=2v^7u^5#.

Answer 2 · 2017-05-08T20:24:35

See a solution process below:

First, use this rule of exponents to rewrite the term on the left of the expression:

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

#(v^color(red)(2))^color(blue)(3) * 2vu^5 => v^(color(red)(2) xx color(blue)(3)) * 2vu^5 => v^6 * 2vu^5#

Next, rewrite this expression as:

#2(v^6 * v)u^5#

Use these two rules of exponents to complete the multiplication:

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

#2(v^color(red)(6) xx v^color(blue)(1))u^5 => 2v^(color(red)(6) + color(blue)(1))u^5 => 2v^7u^5#