Final answer:
To simplify the expression 3√(27x^6y^4), you need to simplify the inside of the square root first by simplifying the numbers and variables separately. Then, combine the simplified parts to get the final answer: 3x^6y^4.
Step-by-step explanation:
To simplify the expression 3√(27x^6y^4), we need to simplify the inside of the square root first. Start by simplifying the numbers inside the square root: 27 is a perfect cube of 3, so we can write it as 3^3. Next, simplify the variables: x^6 can be written as (x^2)^3 and y^4 can be written as (y^2)^2.
Putting it all together, we have 3√(3^3(x^2)^3(y^2)^2). Now we can simplify further by taking the cube root of 3^3, which is 3, and multiplying the exponents: x^(2∙3) is equal to x^6, and y^(2∙2) is equal to y^4. Therefore, the simplified expression is 3x^6y^4.