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(3x^2y^3)^2 Simplify

2 min read Jun 16, 2024
(3x^2y^3)^2 Simplify

Simplifying (3x^2y^3)^2

This expression involves simplifying a term raised to a power. We can use the following rules of exponents to simplify it:

  • (ab)^n = a^n * b^n: This rule states that when we raise a product to a power, we can raise each factor to that power.
  • (a^m)^n = a^(m*n): This rule states that when we raise a power to another power, we multiply the exponents.

Let's apply these rules to simplify (3x^2y^3)^2:

  1. Apply the first rule: We can distribute the exponent of 2 to each factor inside the parentheses: (3x^2y^3)^2 = 3^2 * (x^2)^2 * (y^3)^2

  2. Apply the second rule: We multiply the exponents for each variable: 3^2 * (x^2)^2 * (y^3)^2 = 9 * x^(22) * y^(32)

  3. Simplify: 9 * x^(22) * y^(32) = 9x^4y^6

Therefore, the simplified form of (3x^2y^3)^2 is 9x^4y^6.

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