y^2 fifth root of 64x^6 - 6 fifth root of 2x^6y^10
To simplify the expression y^2 fifth root of 64x^6 - 6 fifth root of 2x^6y^10, you can follow these steps:
Step 1: Simplify the terms inside the fifth root separately.
- The fifth root of 64x^6 can be simplified as the fifth root of 64 times the fifth root of x^6.
The fifth root of 64 is 2 because 2 * 2 * 2 * 2 * 2 = 32.
The fifth root of x^6 is x^(6/5) because (x^(6/5))^5 = x^6.
So, the simplified term is 2x^(6/5).
- The fifth root of 2x^6y^10 can be written as the fifth root of 2 times the fifth root of x^6 times the fifth root of y^10.
The fifth root of 2 remains the same since it cannot be simplified further.
The fifth root of x^6 is x^(6/5).
The fifth root of y^10 is y^(10/5) which simplifies to y^2.
Therefore, the simplified term is 2x^(6/5)y^2.
Step 2: Combine the simplified terms.
- Now that we have simplified both terms inside the fifth roots, the expression becomes:
y^2 * (2x^(6/5) - 6 * 2x^(6/5)y^2).
Step 3: Distribute to simplify the expression further.
- Distribute y^2 to both terms inside the parentheses:
y^2 * 2x^(6/5) - y^2 * 6 * 2x^(6/5)y^2.
- Simplify the first term:
y^2 * 2x^(6/5) = 2y^2x^(6/5).
- Simplify the second term:
y^2 * 6 * 2x^(6/5)y^2 = 12x^(6/5)y^4.
Step 4: Combine the simplified terms.
- Finally, the expression simplifies to:
2y^2x^(6/5) - 12x^(6/5)y^4.
Therefore, the simplified expression is 2y^2x^(6/5) - 12x^(6/5)y^4.