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(2^9x3^5)x(2^4 X 3)^2 Simplified

2 min read Jun 16, 2024
(2^9x3^5)x(2^4 X 3)^2 Simplified

Simplifying (2^9 x 3^5) x (2^4 x 3)^2

This problem involves simplifying an expression with exponents. To do this, we will use the following rules of exponents:

  • 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)

Let's break down the simplification step by step:

  1. Simplify the second factor: (2^4 x 3)^2 = 2^(42) * 3^(12) = 2^8 * 3^2

  2. Combine the factors: (2^9 x 3^5) x (2^8 x 3^2) = 2^(9+8) x 3^(5+2)

  3. Simplify the exponents: 2^(9+8) x 3^(5+2) = 2^17 x 3^7

Therefore, the simplified form of (2^9 x 3^5) x (2^4 x 3)^2 is 2^17 x 3^7.

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