(-2v^7)^3 (-4v^2)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (-2v^7)^3 (-4v^2)^4.

Understanding the Rules of Exponents

Before we dive into the simplification, let's refresh our memory on some key exponent rules:

• Product of Powers: x^m * x^n = x^(m+n)
• Power of a Product: (xy)^n = x^n * y^n
• Power of a Power: (x^m)^n = x^(m*n)

Simplifying the Expression

1. Apply the Power of a Product Rule:

   • (-2v^7)^3 = (-2)^3 * (v^7)^3
   • (-4v^2)^4 = (-4)^4 * (v^2)^4

2. Apply the Power of a Power Rule:

   • (-2)^3 * (v^7)^3 = -8 * v^(7*3) = -8v^21
   • (-4)^4 * (v^2)^4 = 256 * v^(2*4) = 256v^8

3. Multiply the simplified terms:

   • -8v^21 * 256v^8 = -2048v^(21+8) = -2048v^29

Conclusion

Therefore, the simplified form of the expression (-2v^7)^3 (-4v^2)^4 is -2048v^29. Remember to carefully apply the exponent rules to arrive at the correct answer.