Question

Which answer is equivalent to 4 1/3*4 1/6?
a. 16
b .6√​16
c. 2
d. 3√​4

Answer 1

c. 2

Explanation:

`4^(1)/(3)\cdot4^(1)/(6)\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=4^{(1)/(3)+(1)/(6)}=4^{(1\cdot2)/(3\cdot2)+(1)/(6)}=4^{(2)/(6)+(1)/(6)}=4^(2+1)/(6)=4^(3)/(6)=4^(3:3)/(6:3)=4^{(1)/(2)}\\\\\text{use}\ a^(m)/(n)=\sqrt[n]{a^m}\\\\=\sqrt[2]{4^1}=\sqrt4=2`