Question

HELP! Arrange these numeric expressions in ascending order (from the smallest to the largest value).?32^3/5 64^2/3 81^1/4 49^1/2 125^2/3

Answer 1

A1. 32^3/5 = 8

B2. 64^2/3 = 16

C3. 81^1/4 = 3

D4. 49^1/2 = 7

E5. 125^2/3 = 25

C,D,A,B,E.

Answer 2

Answer: The ascending order is given below.

Explanation: We are given five exponents and we are to arrange them in ascending order.

We have

`32^(3)/(5)=\left(2^5\right)^(3)/(5)=2^{5*(3)/(5)}=2^3=8.`

`64^(2)/(3)=\left(2^6\right)^(2)/(3)=2^{6*(2)/(3)}=2^4=16.`

`81^(1)/(4)=\left(3^4\right)^(1)/(4)=3^{4*(1)/(4)}=3.`

`49^(1)/(2)=\left(7^2\right)^(1)/(2)=7^{2*(1)/(2)}=7.`

`125^(2)/(3)=\left(5^3\right)^(2)/(3)=5^{3*(2)/(3)}=5^2=25.`

Since 3 < 7 < 8 <16 < 25, so we have

`81^(1)/(4)<49^(1)/(2)<32^(3)/(5)<64^(2)/(3)<125^(2)/(3).`