Question

2. Justify that √8 3 ∙ √8 3 = √16 using the properties of exponents in at least two different ways.

Answer 1

Explanation:

1st way

`\sqrt[3]{8}* \sqrt[3]{8} = √(16)`

`8^{(1)/(3)}* 8^{(1)/(3)} =16^{(1)/(2)}`

`8^{\left ( (1)/(3)+(1)/(3) \right )} =16^{(1)/(2)}`

`8^{(2)/(3)} =16^{(1)/(2)}`

4 = 4

Hence proved

2nd way

`\sqrt[3]{8}* \sqrt[3]{8} = √(16)`

`\sqrt[3]{8}* \sqrt[3]{8} = \sqrt{4^(2)}`

`8^{(1)/(3)}* 8^{(1)/(3)} = 4^{(2)/(2)}`

`8^{(2)/(3)} = 4^{(2)/(2)}`

`8^{(2)/(3)} = 4`

4 = 4

Hence proved