Express cube root 27x^4y^6 using rational exponents
(27x^4y^6)1/3
(27^1/3)(x^4/3)(y^6/3)
stuck. I think the final answer is 9x^3/4(y^2) I don't know where to put the parentheses to break it up so I hope yall understand what it's suppose to be.
it is wrong. What is the cube root of 27? Hint, it is not 9.
Secondly, the cube root of x^4 is x^(4/3)
By simplify: we get (27)^1/3 * (x^4)^1/3 * (y^6)^1/3 =3y^2x^4/3
To express the cube root of 27x^4y^6 using rational exponents, you can follow these steps:
1. Start by breaking down 27 into its prime factors: 27 = 3 * 3 * 3.
2. Use the property of exponents, which states that (a * b)^n = a^n * b^n, to split the cube root of 27x^4y^6 into separate factors: (27 * x^4 * y^6)^(1/3) = 27^(1/3) * x^(4/3) * y^(6/3).
3. Simplify each component separately:
- The cube root of 27 can be simplified as 27^(1/3) = (3^3)^(1/3) = 3.
- For x^(4/3), you can rewrite it as (x^4)^(1/3) = x^(4/3).
- Similarly, y^(6/3) simplifies to y^(2).
Putting it all together, the expression becomes:
3 * x^(4/3) * y^2.
So, the final answer is 3x^(4/3)y^2.