Question

Justify
`\sqrt[3]{8} * \sqrt[3]{8} = 16`using the properties of exponents in at least two different ways.

Answer 1

EXPLANATION

Given the cubic root:

`\sqrt[3]{8}\cdot\sqrt[3]{8}`

Rewriting 8 as 2^3:

`=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}`

Applying the property of roots:

`\sqrt[3]{a^3}=a`

`=2\cdot2=4`
`\sqrt[3]{8}\cdot\sqrt[3]{8}=\sqrt[3]{8^2}=\sqrt[3]{64}=4`