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

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 $7^x \times 7^{x+7}$.