Explanation:
The expression given in the question is
[tex](\sqrt[3]{64}-16\div2)(2-4)^2[/tex]
Part C:
Step 1:
Solve the cube root
[tex]\begin{gathered} (\sqrt[3]{64}-16\div2)(2-4)^2 \\ (4-16\div2)(2-4)^2 \end{gathered}[/tex]
Step 2:
Divide within first parenthesis
[tex]\begin{gathered} (4-16\div2)(2-4)^2 \\ (4-8)(2-4)^2 \end{gathered}[/tex]
Step 3:
substract within first parenthesis
[tex]\begin{gathered} (4-8)(2-4)^{2} \\ (-4)(-2)^2 \end{gathered}[/tex]
Step 4:
Substract within the parenthesis
[tex]\begin{gathered} (-4)(2-4)^2 \\ -4_(2-4)^2 \\ -4(-2)^2 \end{gathered}[/tex]
Step 5:
Simplify the exponent
[tex]\begin{gathered} -4(-2)^2 \\ =-4(4) \end{gathered}[/tex]
Step 6:
Multiply
[tex]\begin{gathered} -4(4) \\ =-16 \end{gathered}[/tex]
Part A:
The mistake made in step 2 was that the student substracted first instead of dividing with the first parenthesis first
[tex]\begin{gathered} (4-16\div2)(2-4)^2 \\ (-12\div2)(2-4)^2(WRONG) \\ \\ (4-8)(2-4)^2(CORRECT) \end{gathered}[/tex]
Part B:
The mistake made in step 4 was that the student simplified the exponent first instead of substracting with the second parenthesis and then simplifying the exponent
[tex]\begin{gathered} (-4)(2-4)^{2} \\ -6(2-16)(WRONG) \\ \\ -4(-2)^2 \\ -4(4)(CORRECT) \end{gathered}[/tex]
