(2x^3y^4/3xy)^3

2 min read Jun 16, 2024
(2x^3y^4/3xy)^3

Simplifying the Expression (2x^3y^4/3xy)^3

This article will walk through the steps of simplifying the expression (2x^3y^4/3xy)^3.

Understanding the Problem

We have a fraction raised to the power of 3. To simplify this, we need to apply the rules of exponents.

Step 1: Simplifying the Inside of the Parentheses

  • Divide the coefficients: 2/3 = 2/3
  • Divide the x terms: x^3/x = x^(3-1) = x^2
  • Divide the y terms: y^4/y = y^(4-1) = y^3

This leaves us with (2/3)x^2y^3.

Step 2: Applying the Exponent

Now we have ((2/3)x^2y^3)^3. To apply the exponent to the entire expression, we need to distribute it to each part:

  • (2/3)^3 = 8/27
  • (x^2)^3 = x^(2*3) = x^6
  • (y^3)^3 = y^(3*3) = y^9

Final Result

Putting it all together, the simplified expression is (8/27)x^6y^9.

Therefore, (2x^3y^4/3xy)^3 = (8/27)x^6y^9.

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