Expand 2^(2+5): Solving an Exponential Expression

Expand the following equation:

$2^{2+5}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of powers with an equal base (A)

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

00:11 We'll apply this formula to our exercise, in the reverse direction

00:15 We'll break it down into the multiplication of the appropriate powers

00:20 This is the solution

Step-by-Step Solution

To solve this problem, we'll apply the rule for adding exponentials:

Step 1: Identify the base and the exponents.
The base is $2$ and the exponents, when added, are $2 + 5$ .
Step 2: Apply the rule for multiplication of powers.
Using $a^{m+n} = a^m \times a^n$ , we have $2^{2+5} = 2^2 \times 2^5$ .
Step 3: Simplify and expand the expression.
Split the expression into $2^2$ and $2^5$ , which is the expanded form based on the power rule.

Therefore, the expanded form of the equation is $2^2 \times 2^5$ .