How do you simplify #(2x^2y)(5x^-2y^3)# and write it using only positive exponents?

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Answer 1 · 2017-01-25T23:06:30

See the entire simplification process below:

First, rewrite the expression to group like terms:

#(2 xx 5)(x^2 xx x^-2)(y xx y^3)#

Next further simplify using these two rules for exponents:

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

#(2 xx 5)(x^2 xx x^-2)(y^color(red)(1) xx y^3)#

#10x^(2+ -2)y^(1+3)#

#10x^0y^4#

Now, use this rule for exponents to further simplify:

#a^color(red)(0) = 1#

#10 xx 1 xx y^4#

#10y^4#

There is no further simplification required as all of the exponents are positive.