Question

For the following expression, 5^2 (3^8/(3^4 3^5 ))^(-2) Tim evaluates the expression using these steps: Step 1: 5^2 (3^8/3^9 )^(-2) Step 2: 5^2 (3^(-1) )^(-2) Step 3: 5^2 (3^(-3)) Step 4: 25(1/27) Step 5: 25/27 Tim made a mistake. In which step did Tim first make a mistake, and what is the correct expression for that step? Use numbers and words to explain your answer. Step number _____ contains the mistake. Correct expression of that step: __________________________ Explanation:

Answer 1

Step number 2 contains the mistake. The correct expression for that step is 5^2 * (3^-1)^(-2).

In step 2, Tim made a mistake by not applying the exponent rule correctly. The exponent rule states that when you raise a power to another power, you multiply the exponents.

So, when raising (3^-1) to the power of -2, we need to multiply the exponents. (-1) * (-2) = 2. Therefore, the correct expression for that step is 5^2 * 3^2.

To explain it further, in step 1, Tim correctly evaluated 3^8/3^9 as 3^(-1) because when you divide powers with the same base, you subtract the exponents. Then, in step 2, he should have applied the exponent rule correctly to get 3^(-1)^(-2) = 3^2.

The correct expression for step 2 is 5^2 * 3^2.