14x^5y^2 / -21x^2y^8

-2/3x^3 * y^-6

To simplify the expression 14x^5y^2 / -21x^2y^8, we can apply the rules of exponents and division.


1. First, let's simplify the coefficients: 14 / -21 can be reduced by dividing both numbers by 7. This gives us -2 / 3.

2. Next, let's simplify the variable terms with the same base. In this case, we have x and y terms separately. For the x terms, we subtract the exponents: 5 - 2 = 3. After that, for the y terms, we subtract the exponents: 2 - 8 = -6.

3. Now, let's rewrite the expression using the results from the previous steps: (-2 / 3) * x^3 * y^-6.

4. Finally, to write the expression without any negative exponents, we can move the y term with the negative exponent to the denominator. This gives us: (-2 / 3) * x^3 / y^6.

So, the simplified expression is (-2 / 3) * x^3 / y^6.