How do you simplify #(m ^ { 2} n ) ^ { 2} ( 2m n ^ { 3} ) ^ { 3}#?
1 Answer
Expand bracket combine like terms.
Explanation:
All we have to do is expand the bracket and simplify.
#(m^2n)^2(2mn^3)^3#
So first, exponent laws tells us that an exponent of an exponent are multiplied. So let's do that.
#=(m^4n^2)(8m^3n^9)#
Now, exponent laws tells us that an exponent times another exponent (of the same coefficient) are added. We'll do that now.
#=(8m^7n^11)#
And that's all.
We can check our work by subbing in values for both and comparing the results.
In this case, let's say...
=>
=>
#(m^2n)^2(2mn^3)^3#
#=([2]^2[3])^2(2[2][3]^3)^3#
#=([4][3])^2([4][27])^3#
#=(12)^2(108)^3#
#=(144)(1259712)#
#=(144)(1259712)#
#=181398528#
Now for the other one.
#(8m^7n^11)#
#=(8[2]^7[3]^11)#
#=(8[128][177147])#
#=(8[128][177147])#
#=181398528#
We get the same answer. I know there are no restrictions so this is no coincidence - we successfully simplified it!
Hope this helps :)
