%5E2.jpeg "(7xy^2z^5)^2")
Simplifying Expressions with Exponents: (7xy^2z^5)^2
This article will delve into simplifying the expression (7xy^2z^5)^2. We'll break down the process step by step, applying the rules of exponents.
Understanding the Concept
The expression (7xy^2z^5)^2 represents the product of the base (7xy^2z^5) multiplied by itself twice.
Applying the Rules of Exponents
1. Distributing the exponent:
The exponent 2 outside the parentheses applies to each term within the parentheses.
(7xy^2z^5)^2 = 7^2 * x^2 * (y^2)^2 * (z^5)^2
2. Simplifying each term:
- 7^2 = 49
- x^2 remains as x^2
- (y^2)^2 = y^(2*2) = y^4
- (z^5)^2 = z^(5*2) = z^10
3. Combining the simplified terms:
49 * x^2 * y^4 * z^10 = 49x^2y^4z^10
Final Result
Therefore, the simplified form of (7xy^2z^5)^2 is 49x^2y^4z^10.
Key Takeaways
- When an exponent is applied to a product, it is distributed to each factor within the product.
- When an exponent is applied to another exponent, the exponents are multiplied together.
By understanding and applying these rules, we can effectively simplify expressions involving exponents.