Expand b^7: Calculating the Seventh Power Expression

Video Solution

Solution Steps

00:00 Identify which expressions are equal to the original expression

00:03 According to the laws of exponents, multiplying exponents with the same base (A)

00:06 equals the same base raised to the sum of the exponents (N+M)

00:09 We'll apply this formula to our exercise

00:12 We'll maintain the base and add the exponents together

00:16 We can observe that this expression is not equal to the original expression

00:19 We'll use the same method in order to simplify the remaining expressions

00:25 This expression is equal to the original expression

00:34 This expression is not equal to the original expression

00:40 In this case, the exponents are being added together, therefore the formula is not relevant

00:44 This is the solution

Step-by-Step Solution

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 $b^1 \times b^2 \times b^4$ .