1. The problem asks if $-8^{3/4}$ equals the 4th root of $-8^3$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$. 3. First, evaluate $-8^{3/4}$ carefully. The expression means $-(8^{3/4})$ because exponentiation has higher precedence than the negative sign. 4. Calculate $8^{3/4}$: this is the 4th root of $8^3$. 5. Compute $8^3 = 512$. 6. Then, $8^{3/4} = \sqrt[4]{512}$. 7. The 4th root of 512 is $\sqrt[4]{512} = 512^{1/4}$. 8. Since $512 = 2^9$, $512^{1/4} = 2^{9/4} = 2^{2 + 1/4} = 2^2 \times 2^{1/4} = 4 \times 2^{1/4}$. 9. So, $8^{3/4} = 4 \times 2^{1/4}$. 10. Therefore, $-8^{3/4} = - (4 \times 2^{1/4})$. 11. Now, evaluate the 4th root of $-8^3$ which is $\sqrt[4]{-512}$. 12. Since $-512$ is negative, the 4th root of a negative number is not a real number (because even roots of negative numbers are not real). 13. Hence, $\sqrt[4]{-8^3}$ is not a real number, but $-8^{3/4}$ is a negative real number. 14. Therefore, $-8^{3/4} \neq \sqrt[4]{-8^3}$. 15. The statement is False.