A student simplified this expression: (33⋅ 2−4)436

Question

using these steps:

Step 1: 312 ⋅ 2−1636

Step 2: 36216

Step 3: Answer is 0.011

(1 point)
Responses

There is no mistake. The answer is correct.
There is no mistake. The answer is correct.

Step 1 had the mistake. It should have been (6−4)436
Step 1 had the mistake. It should have been the fraction with numerator open paren 6 to the negative 4 power close paren to the 4th power and denominator 3 to the 6th power

Step 2 had the mistake. It should have been 32 =9
Step 2 had the mistake. It should have been 32 =9

Step 3 had the mistake. It should have been 3−2 = 1−2 = 1

Answer 1

Let's revisit the original expression and the student's steps to identify any mistakes.

The original expression is:

$$(33\cdot 2^{-4}{)}^{436}$$

Step 1:

The student wrote

$$312\cdot 2^{-1636}$$

This indicates they likely miscalculated the power or the distribution of terms; with the power of the expression $(a\cdot b{)}^n=a^n\cdot b^n$. Correctly applying this rule, we have:

$$(3^3{)}^{436}\cdot (2^{-4}{)}^{436}=3^{3\cdot 436}\cdot 2^{-4\cdot 436}=3^{1308}\cdot 2^{-1744}$$

So, Step 1 had the mistake.

The correct simplification should be:

$$3^{1308}\cdot 2^{-1744}$$

Step 2:

Then, the student simplified this further to $36216$. Given the previous simplification was incorrect, this step has a mistake too.

The expression $3^{1308}\cdot 2^{-1744}$ does not simplify to $36216$.

Step 3:

The student concludes with $0.011$, which is also incorrect based on the previous simplification steps.

Upon reviewing, we can conclude that:

• Step 1 was incorrect.
• The answer was incorrectly derived from the previous steps.

The correct assertion is:

Step 1 had the mistake. It should have been $(3^3\cdot 2^{-4}{)}^{436}$ which simplifies to $3^{1308}\cdot 2^{-1744}$.

So, the appropriate choice is:

Step 1 had the mistake. It should have been $(3^3\cdot 2^{-4}{)}^{436}$.