Simplifying (7uv^2)^5
In this article, we will explore how to simplify the expression (7uv^2)^5.
Understanding the Rules
To simplify this expression, we need to recall the following rules of exponents:
 Product of Powers: (a^m)^n = a^(m*n)
 Negative Exponent: a^n = 1/a^n
Applying the Rules

Distribute the exponent: Using the product of powers rule, we distribute the exponent 5 to each factor inside the parentheses:
(7uv^2)^5 = 7^5 * u^5 * (v^2)^5

Simplify the negative exponents: Applying the negative exponent rule to each factor:
7^5 * u^5 * (v^2)^5 = 1/7^5 * 1/u^5 * 1/(v^2)^5

Simplify the remaining exponent: Applying the product of powers rule again to the last term:
1/7^5 * 1/u^5 * 1/(v^2)^5 = 1/7^5 * 1/u^5 * 1/v^10

Combine the terms: Finally, we combine all the terms:
1/7^5 * 1/u^5 * 1/v^10 = 1 / (7^5 * u^5 * v^10)
Final Result
Therefore, the simplified form of (7uv^2)^5 is 1 / (7^5 * u^5 * v^10).