Question

Simplify


`( √(5) )( \sqrt[3]{5} )`
a. 5 5/6
b. 5 1/6
c. 5 2/3
d. 5 7/6​

Answer 1

`A.5^{(5)/(6)}`

Explanation:

`We\ are\ given:\\(√(5))(\sqrt[3]{5})\\To\ simplify\ the\ given\ expression\ we\ may\ use\ the\ following\ two\\ 'Laws\ Of\ Exponents'.\\1.\sqrt[n]{a}=a^{(1)/(n)}\\2.m^a*m^b=m^((a+b))\\With\ these\ two\ equations\ we\ can\ proceed\ with\ our\ problem:\\Hence\ following\ Law\ 1,\\√(5)=5^{(1)/(2)} \\\sqrt[3]{5}=5^{(1)/(3)}\\Hence,\\√(5)*\sqrt[3]{5}=5^{(1)/(2)}* 5^{(1)/(3)}\\Hence,\\5^{(1)/(2)}* 5^{(1)/(3)}\\Now,\ by\ using\ Law\ 2,\\`

`5^{((1)/(2)+(1)/(3))}\\=5^{((3+2)/(6))}\\=5^{(5)/(6)}\\`