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(2a^3b^4c^0)^3

2 min read Jun 16, 2024
(2a^3b^4c^0)^3

Simplifying the Expression (2a^3b^4c^0)^3

This article will guide you through simplifying the expression (2a^3b^4c^0)^3.

Understanding the Properties of Exponents

Before we begin, let's recall some important 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)
  • Zero Exponent: x^0 = 1

Simplifying the Expression

  1. Apply the Power of a Product rule: (2a^3b^4c^0)^3 = 2^3 * (a^3)^3 * (b^4)^3 * (c^0)^3

  2. Apply the Power of a Power rule: 2^3 * (a^3)^3 * (b^4)^3 * (c^0)^3 = 2^3 * a^(33) * b^(43) * c^(0*3)

  3. Simplify the exponents: 2^3 * a^(33) * b^(43) * c^(0*3) = 8 * a^9 * b^12 * c^0

  4. Apply the Zero Exponent rule: 8 * a^9 * b^12 * c^0 = 8a^9b^12

Final Result

Therefore, the simplified form of (2a^3b^4c^0)^3 is 8a^9b^12.

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