How do you simplify #\frac { p ^ { 1/ 9} p ^ { 11/ 18} p ^ { 1/ 2} } { ( p ^ { 34} ) ^ { - 1/ 9} }#?

2 Answers

#p^5#

Explanation:

We can use the following rules:

#x^axxx^b=x^(a+b)#
#(x^a)^b=x^(ab)#
#x^-1=1/x#

to rewrite this:

#(p^(1/9)p^(11/18)p^(1/2))/((p^34)^(-1/9)#

to this:

#p^(1/9+11/18+1/2-34(-1/9))#

#p^(2/18+11/18+9/18+68/18)=p^(90/18)=p^5#

Apr 30, 2018

#p^5#

Explanation:

Do not be put off by the fact that this looks difficult.

The normal laws of indices apply, no matter how strange the indices look:

for like bases if you are multiplying #to# add the indices.

#x^m xx x^n = x^(m+n)#

(they are fractions, so follow the fraction rules for adding)

A negative index: #1/x^-m = x^m#

Raising a power to another power #to# multiply the indices:

#(p^(1/9)p^(11/18)p^(1/2))/((p^34)^color(blue)(-1/9))" " =" " p^(1/9)p^(11/18)p^(1/2) xx (p^34)^color(blue)(1/9) #

#=p^(1/9)p^(11/18)p^(1/2) p^(34/9)" "larr# all like bases, add the indices

#=p^((2+11+9+68)/18)" "larr# find a common denominator

#=p^(90/18)#

#=p^5#