Expand b^7: Calculating the Seventh Power Expression

To solve this problem, we'll follow these steps:

• Step 1: Identify the power that needs expansion: $b^7$.
• Step 2: Use the rule for the multiplication of powers to express this as a product of smaller powers of $b$.
• Step 3: Decompose 7 into a sum of smaller numbers and express the power as a product of smaller terms.

Now, let's apply these steps:

Step 1: We have $b^7$ and need to write it as a product of powers.

Step 2: Recall the rule for multiplication of powers, $b^a \times b^b = b^{a+b}$. We will express 7 as the sum of smaller numbers.

Step 3: Choose smaller exponents that add up to 7. Here, we can use $1 + 2 + 4 = 7$. Therefore, $b^7 = b^1 \times b^2 \times b^4$.

Therefore, the expanded form of the expression is $b^1 \times b^2 \times b^4$.