How do you multiply #(u^2v^4)/(uv^3) * (uv)/v * (u^3v^3)/(u^2v)#?

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Answer 1 · 2017-03-02T01:56:34

#u^3v^3#

When multiplying variables with exponents the exponents are added. Remember the following rule: #a^x*a^x = a^(x+x)#

Thus,

#u^2*u*u^3 = u^6# and #v^4*v*v^3 = v^8#
So the numerator is #u^6v^8#

Do the same for the denominator:

#u*u^2 = u^3# and #v^3*v*v = v^5#

Putting it all together:

#(u^6v^8)/(u^3v^5)#

Use the following rule: #a^x/a^x = a^(x-x)#

So the final answer is:
#u^3v^3#

Answer 2 · 2017-03-02T02:08:00

The answer is #u^3v^3#.

First multiply the numerators and denominators together to make one fraction.

#(u^2v^4uvu^3v^3)/(uv^3vu^2v)#

Apply the product rule of exponents #a^ma^n=a^(m+n)#.
Reminder: #a=a^1#

#((u^(2+1+3)v^(4+1+3))/(u^(1+2)v^(3+1+1)))#

Simplify.

#((u^6v^8)/(u^3v^5))#

Apply quotient rule of exponents #a^m/a^n=a^(m-n)#

#(u^(6-3)v^(8-5))#

Simplify.

#u^3v^3#