Evaluate without using a calculator, Write "undefined" of "imaginary" if your result is net a real number, a) \( \sqrt[3]{a^{3}}=\square \square \) b) \( \sqrt[3]{a^{3}}=\square \) c) \( \sqrt[4]{a^{4}}=\square \) d) \( \sqrt{a^{2}}=\square \)

Let’s have fun exploring these problems! a) \( \sqrt[3]{a^{3}} = a \) The cube root of \( a^3 \) is simply \( a \), regardless of whether \( a \) is positive or negative. b) \( \sqrt[3]{a^{3}} = a \) Similar to part (a), taking the cube root of \( a^3 \) results in \( a \) itself! c) \( \sqrt[4]{a^{4}} = |a| \) The fourth root of \( a^4 \) gives us the absolute value of \( a \). This is because \( a \) could be negative, and we take the positive root. d) \( \sqrt{a^{2}} = |a| \) Just like with the fourth root, the square root of \( a^2 \) equals the absolute value of \( a \) to ensure the result is non-negative. In summary, remember: cube roots can handle all numbers, while even roots require taking the absolute value to avoid negatives!