Question

chris tried to rewrite the expression (4^(-2) * 4^(-3))^3. step 1: (4^(-5))^3 step 2: 4^(-2) step 3: 1/4^2 wheres the mistake? did chris make a mistake? if so, in which step? explain your thinking.

Explanation:

Step1: Analyze Step 1

When multiplying powers with the same base ($a^m\cdot a^n=a^{m + n}$), for $(4^{-2}\cdot4^{-3})^3$, inside the parentheses $4^{-2}\cdot4^{-3}=4^{-2+( - 3)}=4^{-5}$, so Step 1 is correct.

Step2: Analyze Step 2

Using the power - of - a - power rule $(a^m)^n=a^{mn}$, for $(4^{-5})^3$, we get $4^{-5\times3}=4^{-15}$. But Chris wrote $4^{-2}$, so Chris made a mistake in Step 2.

Step3: Analyze Step 3

Since Step 2 was incorrect, the result in Step 3 is also incorrect. However, the error originated in Step 2.

Answer:

Chris made a mistake in Step 2.