%5E2.jpeg "(7y^4)^2")
Simplifying (7y^4)^2
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves exponents. Let's break down how to simplify the expression (7y^4)^2.
Understanding Exponents
An exponent indicates how many times a base number is multiplied by itself. In this case, we have:
- Base: 7y^4
- Exponent: 2
This means we are multiplying the entire base (7y^4) by itself twice.
Applying the Power of a Product Rule
To simplify the expression, we can use the Power of a Product Rule. This rule states that when raising a product to a power, we raise each factor to that power. Mathematically, this is represented as:
(ab)^n = a^n * b^n
Applying this rule to our expression:
(7y^4)^2 = 7^2 * (y^4)^2
Applying the Power of a Power Rule
We now have another exponent within our expression: (y^4)^2. To simplify this, we use the Power of a Power Rule. This rule states that when raising a power to another power, we multiply the exponents. Mathematically:
(a^m)^n = a^(m*n)
Applying this rule to our expression:
7^2 * (y^4)^2 = 7^2 * y^(4*2)
Final Simplification
Now, we can simply calculate the remaining exponents:
7^2 * y^(4*2) = 49y^8
Therefore, the simplified form of (7y^4)^2 is 49y^8.