Question

Select the simplification that accurately explains the following statement.

Answer 1

D

Explanation:

1. Use property of exponents:

`(a^b)^c=a^b\cdot ... \cdot a^b\ [\text{ take }c \text{ times } a^b]`

Hence

`(7^{(1)/(3)})^3=7^{(1)/(3)}\cdot 7^{(1)/(3)}\cdot 7^{(1)/(3)}`

2. Use multiplication property of exponents:

`a^b\cdot a^c=a^(b+c)`

Thus,

`7^{(1)/(3)}\cdot 7^{(1)/(3)}\cdot 7^{(1)/(3)}=7^{(1)/(3)+(1)/(3)+(1)/(3)}`

3. Since

`(1)/(3)+(1)/(3)+(1)/(3)=(3)/(3)=1,`

we have that

`7^{(1)/(3)+(1)/(3)+(1)/(3)}=7^1=7`