Task 1: Henry explains why \( 4^{\frac{3}{2}}=8 \) : know that \( 4^{3} \) is 64 and the square root of 64 is 8 . Here is Henrietta's explanation for why \( 4^{\frac{3}{2}}=8 \) : know that \( \sqrt{4}=2 \) and the cube of 2 is 8 . a. Are Henry and Henrietta correct? Explain.

Both Henry and Henrietta are correct in their explanations for why \( 4^{\frac{3}{2}}=8 \), though they approach it differently. Henry's method involves calculating \( 4^3 \) first, which is 64, and then taking the square root of that result, confirming that \( \sqrt{64} = 8 \). Meanwhile, Henrietta breaks it down into two steps: first finding the square root of 4, which is 2, and then cubing that result, as \( 2^3 = 8 \). Both paths lead to the same conclusion! It's really exciting to see the different approaches they took. This reflects a key concept in mathematics: there are often multiple methods to solve a problem. Using exponent rules, \( 4^{\frac{3}{2}} \) can also be expressed as \( (4^{\frac{1}{2}})^3 \), which showcases the elegance of how numbers and operations can interplay to yield the same result in diverse ways!