(2x^3)^3/(-3x^5)^2
To simplify the expression (2x^3)^3/(-3x^5)^2, we first need to apply the exponent to each term inside the parentheses.
For (2x^3)^3, we raise both the coefficient 2 and the variable x^3 to the power of 3. This gives us (2^3) * (x^3)^3 = 8x^9.
For (-3x^5)^2, we square both the coefficient -3 and the variable x^5. This gives us (-3)^2 * (x^5)^2 = 9x^10.
Now we can simplify the expression by dividing 8x^9 by 9x^10.
When dividing variables with the same base, we subtract the exponents. In this case, x^9 divided by x^10 becomes x^(9-10) = x^-1.
Similarly, when dividing numbers, we subtract the exponents as well. 8 divided by 9 becomes 8/9.
Putting it all together, (2x^3)^3/(-3x^5)^2 simplifies to (8/9)x^-1, or 8/9x.
Therefore, the simplified expression is 8/9x.