(7uv^2)^-5

Jasonbradley

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Jun 16, 2024

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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

1. 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

2. 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

3. 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

4. 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).