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(2a^4)^-3 A=0

2 min read Jun 16, 2024
(2a^4)^-3 A=0

Understanding (2a^4)^-3 when a = 0

This expression involves several mathematical concepts: exponents, negative exponents, and substitution. Let's break it down step-by-step.

Exponents and Negative Exponents

  • Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times (2 * 2 * 2 = 8).
  • Negative Exponents: A negative exponent means taking the reciprocal of the base raised to the positive version of the exponent. For example, 2^-3 is the same as 1/(2^3) = 1/8.

Applying the Concepts

  1. Simplify the exponent: (2a^4)^-3 can be simplified using the rule that states (x^m)^n = x^(mn). Therefore, (2a^4)^-3 = 2^-3 * a^(4-3) = 2^-3 * a^-12.

  2. Apply the negative exponent rule: 2^-3 = 1/(2^3) = 1/8 and a^-12 = 1/(a^12).

  3. Substitute a = 0: Now, we substitute a = 0 into the simplified expression: (1/8) * (1/(0^12)).

  4. Evaluate: 0 raised to any power (except 0) is always 0. Therefore, 0^12 = 0. This results in the expression: (1/8) * (1/0).

  5. Division by Zero: Division by zero is undefined in mathematics.

Conclusion:

When a = 0, the expression (2a^4)^-3 becomes undefined due to division by zero. This is a crucial point to understand when dealing with expressions involving variables and exponents, as the value of the variable can significantly impact the outcome.

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