%5E4.jpeg "(a^2b^3b)^4")
Simplifying the Expression (a^2b^3b)^4
The expression (a^2b^3b)^4 can be simplified using the rules of exponents. Here's a breakdown of the steps:
1. Combine Like Terms:
- b^3b simplifies to b^4 because when multiplying exponents with the same base, you add the powers.
The expression now becomes (a^2b^4)^4.
2. Apply the Power of a Product Rule:
- (ab)^n = a^n * b^n This rule states that when raising a product to a power, you raise each factor to that power.
Applying this to our expression:
(a^2b^4)^4 = a^(24) * b^(44)
3. Simplify the Exponents:
- a^(2*4) = a^8
- b^(4*4) = b^16
The final simplified expression is a^8b^16.
Summary:
By applying the rules of exponents, we can simplify the complex expression (a^2b^3b)^4 to a much simpler form: a^8b^16. This process demonstrates the importance of understanding exponent rules for efficient algebraic manipulation.