How do you simplify #5x ^ { 2} y ^ { 3} \times 10x y ^ { 9}#?
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"Find the sum of the integers between 2 and 100 which are divisible by 3 ?"
First, you multiply #5 xx 10# to get #50#. Then you have to add the exponents. So for #x#, it would be #2 + 1# (there is an imaginary #1# exponent on the other #x#), which would make it #x^3#.
For y, you would do the same thing, #3 + 9 = 12#.
So, it would look like this.
#5x^2y^3 xx 10xy^9#
#= 5x^2y^3 xx 10x^1y^9#
#= 50x^2y^3 xx x^1y^9#
#= 50 x^2 xx x^1 xx y^3 xx y^9#-
This is grouping the terms, making it easier to add them. When you do this, just add the exponents.
#= 50 x^3y^12#
#5x^2y^3xx10xy^9=color(blue)(50x^3y^12#
Simplify:
#5x^2y^3xx10xy^9#
Multiply the coefficients.
#5xx6xxx^2y^3xy^9#
Simplify.
#50x^2y^3xy^9#
Combine similar variables.
#50x^(2)xy^3y^9#
Apply the product rule of exponents: #a^ma^n=a^(m+n)#. No exponent is understood to be #1#.
#50x^(2+1)y^(3+9)#
Simplify.
#50x^3y^12#
