Question

Order the simplification steps of the expression below using the properties of rational exponents.
`\sqrt[3]{7}=7^{(1)/(3)}`

A.)
`\left(7^{(1)/(3)}\right)^3=7^{(1)/(3)}\cdot 7^{(1)/(3)}\cdot 7^{(1)/(3)}=7^{(1)/(3)}\cdot ^{(1)/(3)}\cdot ^{(1)/(3)}=7^{(3)/(3)}=7^1=7\\`

B.)
`\left(7^{(1)/(3)}\right)^3=7^{(1)/(3)}\cdot 7^{(1)/(3)}\cdot 7^{(1)/(3)}=7\cdot 7^{(1)/(3)}=3\cdot (1)/(3)\cdot 7=1\cdot 7=7`

C.)
`\left(7^{(1)/(3)}\right)^3=7^{(1)/(3)}\cdot \:7^{(1)/(3)}\cdot \:7^{(1)/(3)}=7^{(1)/(3)}+\:^{(1)/(3)}+\:^{(1)/(3)}=7^{(3)/(3)}=7^1=7`

D.)
`\left(7^{(1)/(3)}\right)^3=7^{(1)/(3)}\cdot \:7^{(1)/(3)}\cdot \:7^{(1)/(3)}=7\cdot \left((1)/(3)+(1)/(3)+(1)/(3)\right)=7\cdot (3)/(3)=7\cdot 1=7`

Answer 1

The answer is C.)
`\left(7^{(1)/(3)}\right)^3=7^{(1)/(3)}\cdot \:7^{(1)/(3)}\cdot \:7^{(1)/(3)}=7^{(1)/(3)+(1)/(3)+(1)/(3)}=7^{(3)/(3)}=7^1=7`

what you plug in for calculator

\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7