Expand 7^6: Calculate the Sixth Power of Seven

To solve this problem, let's examine the possible answer choices to determine which ones equal $7^6$.

• **Choice 1:** $7^1 \times 7^2 \times 7^4$
  By exponent rules: $7^1 \cdot 7^2 \cdot 7^4 = 7^{1+2+4} = 7^7$.
• **Choice 2:** $7^1 \times 7 \times 7^4$
  Here, $7 = 7^1$. So, $7^1 \cdot 7^1 \cdot 7^4 = 7^{1+1+4} = 7^6$.
• **Choice 3:** $7^2 \times 7^2 \times 7^2$
  Using the rule: $7^2 \cdot 7^2 \cdot 7^2 = 7^{2+2+2} = 7^6$.
• **Choice 4:** This states choices 'b + c are correct'.

After calculations, choices 2 and 3 simplify to $7^6$. Therefore, the correct answer is indeed that choices 'b+c are correct'. Thus, the correct choice is:

Choice 4: b+c are correct