Question

QUICK ILL GIVE BRAINLIESTA student simplified (cube root of 64 − 16 ÷ 2)(2 − 4)2 using the following steps:(cube root of 64 − 16 ÷ 2)(2 − 4)2Step 1: (4 − 16 ÷ 2)(2 − 4)2 Simplify the cube root.Step 2: (−12 ÷ 2)(2 − 4)2 Subtract within first parentheses.Step 3: −6(2 − 4)2 Divide within the first parentheses.Step 4: −6(2 − 16) Simplify the exponent.Step 5: −6(−14) Subtract within the parentheses.Step 6: 84 Multiply.Part A: The student made a mistake in Step 2. Describe the mistake and explain how to correct it.Part B: The student made a mistake in Step 4. Describe the mistake and explain how to correct it.Part C: Show every step of your work to simplify (cube root of 64 − 16 ÷ 2)(2 − 4)2.

Answer 1

Explanation:

The expression given in the question is

$(\sqrt[3]{64}-16\div2)(2-4)^2$

Part C:

Step 1:

Solve the cube root

$\begin{gathered} (\sqrt[3]{64}-16\div2)(2-4)^2 \\ (4-16\div2)(2-4)^2 \end{gathered}$

Step 2:

Divide within first parenthesis

$\begin{gathered} (4-16\div2)(2-4)^2 \\ (4-8)(2-4)^2 \end{gathered}$

Step 3:

substract within first parenthesis

$\begin{gathered} (4-8)(2-4)^{2} \\ (-4)(-2)^2 \end{gathered}$

Step 4:

Substract within the parenthesis

$\begin{gathered} (-4)(2-4)^2 \\ -4_(2-4)^2 \\ -4(-2)^2 \end{gathered}$

Step 5:

Simplify the exponent

$\begin{gathered} -4(-2)^2 \\ =-4(4) \end{gathered}$

Step 6:

Multiply

$\begin{gathered} -4(4) \\ =-16 \end{gathered}$

Part A:

The mistake made in step 2 was that the student substracted first instead of dividing with the first parenthesis first

$\begin{gathered} (4-16\div2)(2-4)^2 \\ (-12\div2)(2-4)^2(WRONG) \\ \\ (4-8)(2-4)^2(CORRECT) \end{gathered}$

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

$\begin{gathered} (-4)(2-4)^{2} \\ -6(2-16)(WRONG) \\ \\ -4(-2)^2 \\ -4(4)(CORRECT) \end{gathered}$