Expand the Power: Solving 7^(2x+7) Step by Step

Expand the following equation:

$7^{2x+7}=$

Video Solution

Solution Steps

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

00:04 According to the laws of exponents, the multiplication of powers with the same base (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:11 We will apply this formula to our exercise

00:14 We'll maintain the base and add the exponents together

00:18 We can observe that this expression is not equal to the original expression

00:27 We will use the same method in order to simplify the remaining expressions

00:31 In this expression the operation is addition and not multiplication, therefore it's not relevant

00:40 This expression is not equal to the original expression

00:55 This expression is equal to the original expression

01:00 This is the solution

Step-by-Step Solution

To tackle this problem, we need to expand the expression $7^{2x+7}$ using the properties of exponents:

Step 1: Identify the structure of the exponent in the form $2x + 7$ .
Step 2: Recognize this as a sum of two components: $2x$ and $7$ .
Step 3: Apply the exponent rule $a^{m+n} = a^m \times a^n$ to separate the expression into two distinct exponent terms.

Now, let's proceed with the solution:

Step 1: Given the exponent is $2x + 7$ , break it down into individual components:
$2x + 7 = x + x + 7$ .

Step 2: Applying the rule $a^{m+n} = a^m \times a^n$ :
$7^{2x+7} = 7^{x+x+7} = 7^x \times 7^{x+7}$ .

Therefore, the expanded form of the expression is $7^x \times 7^{x+7}$ .