%5E2*12ab%5E4%2F5a%5E7b%5E3%2B3a%5E7b%5E3.jpeg "(2a^5b^3)^2*12ab^4/5a^7b^3+3a^7b^3")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the simplification of the following algebraic expression:
(2a^5b^3)^2 * 12ab^4 / 5a^7b^3 + 3a^7b^3
Let's break down the steps involved in simplifying this expression:
1. Applying the Power Rule
First, we need to simplify the term (2a^5b^3)^2. We can apply the power rule for exponents, which states that (x^m)^n = x^(m*n).
Applying this rule:
(2a^5b^3)^2 = 2^2 * (a^5)^2 * (b^3)^2 = 4a^10b^6
2. Simplifying Multiplication and Division
Now, let's simplify the entire expression by multiplying and dividing terms:
(4a^10b^6) * 12ab^4 / 5a^7b^3 + 3a^7b^3
- Multiply the numerators: 4a^10b^6 * 12ab^4 = 48a^11b^10
- Divide by the denominator: 48a^11b^10 / 5a^7b^3 = (48/5)a^4b^7
Our expression now looks like this:
(48/5)a^4b^7 + 3a^7b^3
3. Combining Like Terms
Since the terms have different exponents, we cannot combine them directly.
Therefore, the simplified form of the expression is (48/5)a^4b^7 + 3a^7b^3.