(3ab^2c)^2(-2a^2b^4)^2(a^4c^2)^3(a^2b^4c^5)^2(2a^3b^2c^4)^3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

Let's simplify the following expression:

(3ab^2c)^2(-2a^2b^4)^2(a^4c^2)^3(a^2b^4c^5)^2(2a^3b^2c^4)^3

To simplify this expression, we'll use the following rules of exponents:

• (a^m)^n = a^(m*n)
• (ab)^n = a^n * b^n
• a^m * a^n = a^(m+n)

Step 1: Apply the first rule to each term in the expression.

This gives us:

• 3^2 a^2 b^4 c^2 * (-2)^2 a^4 b^8 * a^12 c^6 * a^4 b^8 c^10 * 2^3 a^9 b^6 c^12

Step 2: Combine like terms.

This means multiplying the coefficients together and adding the exponents of the same variables:

• (9 * 4 * 8) * a^(2+4+12+4+9) * b^(4+8+8+6) * c^(2+6+10+12)

Step 3: Simplify the expression.

• 288 * a^31 * b^26 * c^30

Therefore, the simplified expression is 288a^31b^26c^30.