How do you simplify #\frac { a ^ { \frac { 1} { 3} } } { a ^ { \frac { 1} { 4} } a ^ { - \frac { 1} { 2} } }#?

Question

595 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-04T12:22:49

#a^{7/12}#

#a^i a^j = a^{i + j}#

#a^i / a^j = a^{i - j}#

Then, #a^i / (a^j a^k) = a^{i - j - k}#

#a^{1/3 - 1/4 + 1/2} = a^{(4-3+6)/12}#

Answer 2 · 2017-04-04T12:24:59

I tried using some properties of exponents:

We can use several properties of exponents such as:
#a^xa^y=a^(x+y)#
and write:
#(a^(1/3))/(a^(1/4-1/2))=(a^(1/3))/(a^(-1/4))=#

Then we can use the fact that:
#a^x/a^y=a^(x-y)# and write:
#(a^(1/3))/(a^(-1/4))=a^(1/3+1/4)=a^(7/12)=#

Then we use the fact that: #x^(y/x)=rootx(a^y)# and write:
#a^(7/12)=root12(a^7)#