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(10^2)^-3

less than a minute read Jun 16, 2024
(10^2)^-3

Simplifying (10^2)^-3

Let's break down how to simplify the expression (10^2)^-3.

Understanding the Rules

We'll use two key rules of exponents:

  1. Power of a Power: (a^m)^n = a^(m*n)
  2. Negative Exponent: a^-n = 1/a^n

Applying the Rules

  1. Apply the Power of a Power rule: (10^2)^-3 = 10^(2 * -3)

  2. Simplify the exponent: 10^(2 * -3) = 10^-6

  3. Apply the Negative Exponent rule: 10^-6 = 1/10^6

  4. Calculate the final result: 1/10^6 = 1/1,000,000

Conclusion

Therefore, (10^2)^-3 simplifies to 1/1,000,000. Remember to apply the rules of exponents systematically to solve these kinds of expressions.

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