Simplify by taking roots of the numerator and the denominator assume that all expressions under radicals represent positive numbers 3square 27x^8/y^3
how much longer is three 12m planks of wood than four 8m planks of wood
4 m?
To simplify the expression 3√(27x^8/y^3), we can take the cube root of 27, the square root of x^8, and the cube root of y^3 individually.
Step 1: Simplify the numerator.
The cube root of 27 = 3, because 3^3 = 27.
The square root of x^8 = x^(8/2) = x^4, because (x^4)^2 = x^8.
So, the numerator simplifies to 3x^4.
Step 2: Simplify the denominator.
The cube root of y^3 = y^(3/3) = y^1 = y, because y^1 = y.
So, the denominator simplifies to y.
Putting it all together, the simplified expression is:
3x^4/y