Let's evaluate: $-\frac{8}{2^{\frac{8}{3}}}-2^{\frac{4}{3}}$

ⓘ Dividing powers with the same base subtracts the exponents: $-\frac{8}{2^{\frac{8}{3}}}$ = $-\frac{2^3}{2^{\frac{8}{3}}}$ = $-2^{3-\frac{8}{3}}$ = $-2^{\frac{1}{3}}$■Split the exponent into its integer part and a remainder: a sum of exponents gives a product of powers, and an exponent m/n is the root of order n of the power m: $2^{\frac{4}{3}}$ = $2^{1+\frac{1}{3}}$ = $2^1\times 2^{\frac{1}{3}}$ = $2\times \sqrt[3]{2}$

$-2^{\frac{1}{3}}-2\times \sqrt[3]{2}$

ⓘ Like terms are grouped by adding their coefficients: $-2^{\frac{1}{3}}-2\times \sqrt[3]{2}$ = $-3\times \sqrt[3]{2}$

▶Result:   $-3\times \sqrt[3]{2}$

The numeric value of: $-3\times \sqrt[3]{2}$ equals:

$-3\times \approx 1.2599$

▷ $\approx -3.7798$