How do you use the laws of exponents to simplify the expression #(6y^3)^4/(2y^5)#?

Question

4255 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-09T20:45:06

The Laws of Exponents relevant here are
1. #(bc)^m = b^m*c^m#
2. #(b^m)^n = b^(mn)#
3. #b^(-m) = 1/(b^m)#
4. #b^m*b^n = b^(m+n)#

#(((6y)^3)^4)/(2y^5)#

#= ((6y)^12)/(2y^5) " by Rule [2]"#

#= (6^12*y^12)/(2y^5) " by Rule [1]"#

#=6^12/2 * y^12*y^(-5) " by Rule [3]"#

#= 6^12/2y^7 " by Rule [4]"#

You could evaluate #6^12/2# but that's just arithmetic.