(2u^4/4uv^-5)^-3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Negative Exponents

This article will guide you through simplifying the expression (2u^4/4uv^-5)^-3.

Understanding the Rules

To simplify this expression, we need to utilize the following rules of exponents:

• Product of powers: x^m * x^n = x^(m+n)
• Quotient of powers: x^m / x^n = x^(m-n)
• Power of a power: (x^m)^n = x^(m*n)
• Negative exponent: x^-n = 1/x^n

Step-by-Step Simplification

1. Distribute the negative exponent: (2u^4/4uv^-5)^-3 = 1 / (2u^4/4uv^-5)^3

2. Apply the power of a power rule: 1 / (2u^4/4uv^-5)^3 = 1 / (2^3 u^(43) / 4^3 u^3 v^(-53))

3. Simplify the exponents: 1 / (2^3 u^(43) / 4^3 u^3 v^(-53)) = 1 / (8u^12 / 64u^3 v^-15)

4. Simplify the coefficients: 1 / (8u^12 / 64u^3 v^-15) = 1 / (u^12 / 8u^3 v^-15)

5. Apply the quotient of powers rule: 1 / (u^12 / 8u^3 v^-15) = 8u^3 v^-15 / u^12

6. Apply the quotient of powers rule again: 8u^3 v^-15 / u^12 = 8u^(3-12) v^-15 = 8u^-9 v^-15

7. Apply the negative exponent rule: 8u^-9 v^-15 = 8 / (u^9 v^15)

Final Result

Therefore, the simplified form of the expression (2u^4/4uv^-5)^-3 is 8 / (u^9 v^15).