(14a^4b^3-20a^2b^2+2ab)*(2ab)^-1

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (14a^4b^3 - 20a^2b^2 + 2ab) * (2ab)^-1

This problem involves simplifying an expression with exponents and variables. Let's break it down step-by-step:

Understanding the problem:

• (14a^4b^3 - 20a^2b^2 + 2ab): This is a polynomial with three terms.
• (2ab)^-1: This is a monomial raised to a negative exponent.

Simplifying the expression:

1. Simplify the monomial with a negative exponent:

   • Recall that a term raised to a negative exponent is the same as its reciprocal with a positive exponent.
   • Therefore, (2ab)^-1 = 1 / (2ab)

2. Apply the distributive property:

   • Multiply each term in the polynomial by 1/(2ab):
     • (14a^4b^3 / 2ab) - (20a^2b^2 / 2ab) + (2ab / 2ab)

3. Simplify each term:

   • (14a^4b^3 / 2ab) = 7a^3b^2
   • (20a^2b^2 / 2ab) = 10ab
   • (2ab / 2ab) = 1

4. Combine the simplified terms:

   • 7a^3b^2 - 10ab + 1

Therefore, the simplified form of the expression (14a^4b^3 - 20a^2b^2 + 2ab) * (2ab)^-1 is 7a^3b^2 - 10ab + 1.