Question #9e52a

1 Answer
Sep 30, 2016

The product rule and the power rules in question are

  • #a^mxxa^n = a^(m+n)#

  • #a^m-:a^n = a^(m-n)#

  • #(a^m)^n = a^(mxxn)#

(Note that the second rule comes directly from the first, because #1/a^x = a^(-x)#, so #a^m/a^n = a^mxxa^(-n) = a^(m+(-n)) = a^(m-n)#)

Rather than simply post answers to all of the questions on the worksheet, here are a couple of examples of each. These should show how to do the rest, as the problems are all effectively the same, save for the changed values.


First set:

1) #5^(-8)xx5^(-5) = 5^(-8+(-5)) = 5^(-13)#

2) #18^(-4)xx18^(3) = 18^(-4+3)=18^(-1)#


Second set:

1) #4^2-:4^10 = 4^(2-10) = 4^(-8)#

2) #19^7 -: 19^(-8) = 19^(7-(-8)) = 19^15#


Third set:

1)#(15^9)^(-7) = 15^(9xx-7)=15^(-63)#

2)#(7^3)^6 = 7^(3xx6)=7^18#