4-in-exponential-form.jpeg "(2a)4 In Exponential Form")
Understanding (2a)⁴ in Exponential Form
In mathematics, we use exponents to represent repeated multiplication. Let's break down how to express (2a)⁴ in exponential form.
What is an exponent?
An exponent tells us how many times a base number is multiplied by itself. For example, in 2⁴, 2 is the base and 4 is the exponent. This means we multiply 2 by itself four times: 2 * 2 * 2 * 2 = 16.
Applying the exponent to (2a)⁴
In (2a)⁴, the base is the entire expression (2a). This means we're multiplying (2a) by itself four times:
(2a)⁴ = (2a) * (2a) * (2a) * (2a)
Simplifying the expression
To simplify this, we apply the distributive property of multiplication:
(2a) * (2a) * (2a) * (2a) = 2 * a * 2 * a * 2 * a * 2 * a
Now we can rearrange the terms and group like terms:
2 * 2 * 2 * 2 * a * a * a * a = 2⁴ * a⁴
Final Answer
Therefore, the exponential form of (2a)⁴ is 2⁴a⁴. This can be further simplified as 16a⁴.