(m^5n/pq^2)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Exponential Expressions: (m^5n/pq^2)^4

This article will delve into simplifying the expression (m^5n/pq^2)^4. We will use the rules of exponents to break down the expression and arrive at a simplified form.

Understanding the Rules of Exponents

Before we begin, let's review the key rules of exponents that we'll be applying:

• Power of a Product: (ab)^n = a^n * b^n
• Power of a Quotient: (a/b)^n = a^n / b^n
• Power of a Power: (a^m)^n = a^(m*n)

Simplifying the Expression

1. Apply the Power of a Quotient rule:

   (m^5n/pq^2)^4 = (m^5n)^4 / (pq^2)^4

2. Apply the Power of a Product rule to both numerator and denominator:

   (m^5n)^4 / (pq^2)^4 = (m^5)^4 * (n)^4 / (p)^4 * (q^2)^4

3. Apply the Power of a Power rule to each term:

   (m^5)^4 * (n)^4 / (p)^4 * (q^2)^4 = m^(54) * n^4 / p^4 * q^(24)

4. Simplify the exponents:

   m^(54) * n^4 / p^4 * q^(24) = m^20 * n^4 / p^4 * q^8

Final Result

Therefore, the simplified form of the expression (m^5n/pq^2)^4 is m^20 * n^4 / p^4 * q^8.