(Originais Teachy 2023) - Question Medium of Mathematics

Maria is studying exponentiation with rational exponents, and her teacher explained that she can represent roots using fractional exponents. To practice and deepen her understanding, Maria decides to create different mathematical expressions. To help Maria with this task, her friends Henrique and Ana decided to help her with suggestions of expressions mixing exponentiation and radical expressions. Based on this, (a) Write a mathematical expression that combines exponentiation, radical expressions, and rational exponents, following Henrique's example, who combined the square root with an exponent of 1/2; (b) Write another mathematical expression that also combines exponentiation, radical expressions, and rational exponents, but this time, following Ana's example who used the cube root and an exponent of 1/3; (c) Determine the answers to the proposed expressions in items (a) and (b), remembering to simplify the expressions whenever possible.