Question

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

Answer 1

Step-by-step explanation:

1st way

$\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{16}$

$8^{\frac{1}{3}}\times 8^{\frac{1}{3}} =16^{\frac{1}{2}}$

$8^{\left ( \frac{1}{3}+\frac{1}{3} \right )} =16^{\frac{1}{2}}$

$8^{\frac{2}{3}} =16^{\frac{1}{2}}$

4 = 4

Hence proved

2nd way

$\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{16}$

$\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{4^{2}}$

$8^{\frac{1}{3}}\times 8^{\frac{1}{3}} = 4^{\frac{2}{2}}$

$8^{\frac{2}{3}} = 4^{\frac{2}{2}}$

$8^{\frac{2}{3}} = 4$

4 = 4

Hence proved