Expand the Expression: Solving 2^(2a+a) Step by Step

Expand the following equation:

$2^{2a+a}=$

Video Solution

Solution Steps

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

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

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

00:10 We will apply this formula to our exercise

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

00:19 We can observe that this expression is not equal to the original expression

00:26 We will use the same method in order to simplify the remaining expressions

00:33 This expression is equal to the original expression

00:36 In this expression the operation is addition and not multiplication, therefore it's not relevant

00:41 This is the solution

Step-by-Step Solution

To solve the problem, we can follow these steps:

Step 1: Recognize that the given expression is $2^{2a+a}$ .
Step 2: Use the Power of a Power Rule for exponents, which allows us to write $a^{m+n} = a^m \times a^n$ .
Step 3: Rewrite the expression as follows:

Given: $2^{2a+a}$

Step 4: Simplify the exponent by splitting it:

Since the expression in the exponent is $2a+a$ , we can write:

$2^{2a+a} = 2^{2a} \times 2^a$

Thus, applying the properties of exponents correctly leads us to the expanded form.

Therefore, the expanded equation is $2^{2a} \times 2^a$ .