Question

If $x^6=20$, what is $x^8$?

• A. $400\times \sqrt[3]{320}$
• B. $10\times \sqrt{20}$
• C. $20\times \sqrt{20}$
• D. $20\times \sqrt[3]{320}$
• E. $\sqrt[3]{320}$

Answer 1

Answer: (D)

$20\times \sqrt[3]{320}$

Given, $x^6=20$

$\Rightarrow x=\sqrt[6]{620}={20}^{\frac{1}{6}}$

Now, $x^8={20}^{\frac{8}{6}}$

$={20}^{\frac{4}{3}}={20}^{1+\frac{1}{3}}$

$=20\times \sqrt[3]{320}$