How do you simplify #(20b^10) /( 10b^20)#?

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Answer 1 · 2018-05-27T14:06:49

#2b^-10#

You can split the fraction into two:
#20/10# and #b^10/b^20# And you can work out each separate.

#20/10=2#

Using the formula
#a^b/a^c=a^(b-c)# you can work out the second fraction.

#b^10/b^20=b^(10-20)=b^-10#

Then you can multiply #2# by #b^-10# to get #2b^-10#

Answer 2 · 2018-05-27T14:16:29

#2/b^10#

#(20b^10)/(10b^20)#

#(2 xx 10 xx b^10)/(1 xx 10 xx b^20)#

#(2 xx cancel10 xx b^10)/(1 xx cancel10 xx b^20)#

#(2 xx 1 xx b^10)/(1 xx 1 xx b^20)#

#(2b^10)/b^20#

#2b^10 div b^20#

Recall;

#x^a div x^b = x^(a - b)#

Hence;

#2b^10 div b^20 = 2b^(10 - 20)#

#2b^-10#

But: #x^-1 = 1/x#

Therefore;

#2/b^10#

Answer 3 · 2018-05-27T14:28:03

#2b^-10#

#(20b^10)/(10b^20)#

It might be helpful to rewrite this as two separate fractions.

#20/10 * b^10/b^20#

#2 * b^10/b^20#

We can simplify the second fraction if we remember a little rule: #n^a/n^b = n^(a-b)#. In other words, #b^10/b^20# will equal #b^(10-20)# or #b^-10#.

#2*b^-10#

#2b^-10#