Jasonbradley
Home

(3a^-4/2b^-3)^-2*10a^7b^3

3 min read Jun 16, 2024
(3a^-4/2b^-3)^-2*10a^7b^3

Simplifying the Expression: (3a^-4/2b^-3)^-2 * 10a^7b^3

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

Understanding the Rules

Before we start, let's recall the key rules of exponents:

  • Product of Powers: x^m * x^n = x^(m+n)
  • Quotient of Powers: x^m / x^n = x^(m-n)
  • Power of a Power: (x^m)^n = x^(m*n)
  • Negative Exponent: x^-n = 1/x^n

Simplifying the Expression

  1. Simplify the Inner Parenthesis:

    (3a^-4/2b^-3)^-2 = (3/2 * a^-4 * b^3)^-2

  2. Apply Power of a Power Rule:

    (3/2 * a^-4 * b^3)^-2 = (3/2)^-2 * (a^-4)^-2 * (b^3)^-2 = (2/3)^2 * a^8 * b^-6

  3. Simplify the Numerator:

    (2/3)^2 * a^8 * b^-6 = 4/9 * a^8 * b^-6

  4. Combine with the Remaining Term:

    (4/9 * a^8 * b^-6) * 10a^7b^3 = (4/9 * 10) * a^8 * a^7 * b^-6 * b^3

  5. Apply Product of Powers Rule:

    (40/9) * a^(8+7) * b^(-6+3) = (40/9) * a^15 * b^-3

  6. Apply Negative Exponent Rule:

    (40/9) * a^15 * b^-3 = (40/9) * a^15 * (1/b^3)

  7. Final Simplified Expression:

    40a^15 / 9b^3

Conclusion

Therefore, the simplified form of the expression (3a^-4/2b^-3)^-2 * 10a^7b^3 is 40a^15 / 9b^3. By applying the rules of exponents step-by-step, we successfully simplified the expression.

Related Post

Featured Posts