#1. rewrite 36 1/2 as an integer #2. Use the rational exponent property to rewrite 27 2/3 as an integer.

Question

asked Feb 12, 2019 71.6k views

1 Answer

Robert Robinson · Answer 1 · 2019-02-17T04:30:47+0000

(1)

we are given

$(36)^{(1)/(2) }$

Firstly, we will find all possible factors of 36

36=6*6=6^2

we can write as

$(36)^{(1)/(2) }=(6^2)^{(1)/(2) }$

now, we can use property of exponent

(a^m)^n=a^(m*n)

we get

$(36)^{(1)/(2) }=(6)^{2*(1)/(2) }$

$(36)^{(1)/(2) }=(6)^(1 )$

$(36)^{(1)/(2) }=6$ ..............Answer

(2)

$(27)^{(2)/(3) }$

Firstly, we will find all possible factors of 27

27=3*3*3=3^3

we can write as

$(27)^{(2)/(3) }=(3^3)^{(2)/(3) }$

now, we can use property of exponent

(a^m)^n=a^(m*n)

we get

$(27)^{(2)/(3) }=(3)^{3*(2)/(3) }$

$(27)^{(2)/(3) }=(3)^(2 )$

$(27)^{(2)/(3) }=3*3$

$(27)^{(2)/(3) }=9$ ..................Answer