(4s^5t^-7/-2s^-2t^4)^3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents: (4s^5t^-7/-2s^-2t^4)^3

This article will walk through the steps of simplifying the expression (4s^5t^-7/-2s^-2t^4)^3.

Understanding the Rules of Exponents

Before we begin, let's review a few key 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)
• Power of a product: (x*y)^n = x^n * y^n
• Power of a quotient: (x/y)^n = x^n / y^n

Simplifying the Expression

1. Apply the power of a quotient rule:

   (4s^5t^-7/-2s^-2t^4)^3 = (4^3 * (s^5)^3 * (t^-7)^3) / (-2^3 * (s^-2)^3 * (t^4)^3)

2. Apply the power of a power rule:

   (4^3 * s^(53) * t^(-73)) / (-2^3 * s^(-23) * t^(43))

3. Simplify the exponents:

   (64 * s^15 * t^-21) / (-8 * s^-6 * t^12)

4. Apply the quotient of powers rule:

   64/-8 * s^(15-(-6)) * t^(-21-12)

5. Simplify further:

   -8 * s^21 * t^-33

6. Express negative exponents in the denominator:

   -8s^21 / t^33

Final Answer

Therefore, the simplified form of (4s^5t^-7/-2s^-2t^4)^3 is -8s^21 / t^33.