Question

1. $(sqrt5{8})^4$

Explanation:

Step1: Rewrite root as exponent

$\sqrt[5]{8} = 8^{\frac{1}{5}}$

Step2: Apply exponent power rule

$(8^{\frac{1}{5}})^4 = 8^{\frac{4}{5}}$

Step3: Rewrite 8 as power of 2

$8 = 2^3$, so $8^{\frac{4}{5}} = (2^3)^{\frac{4}{5}}$

Step4: Simplify the exponent

$(2^3)^{\frac{4}{5}} = 2^{\frac{12}{5}}$

Step5: Optional: Rewrite as mixed radical

$2^{\frac{12}{5}} = 2^{2+\frac{2}{5}} = 2^2 \times 2^{\frac{2}{5}} = 4\sqrt[5]{4}$

Answer:

$2^{\frac{12}{5}}$ or $4\sqrt[5]{4}$