Use rational exponents to write x1/6*y1/5*z1/4 as a single radical expression
The LCM of 4,5,6 = 60
so, we'd have
(x^10 y^12 z^15)^(1/60)
To write x^(1/6) * y^(1/5) * z^(1/4) as a single radical expression, we need to simplify each exponent and then combine them together.
Let's start by simplifying each exponent:
x^(1/6) can be written as the 6th root of x, because raising a number to the power of 1/n is the same as taking the n-th root of that number.
y^(1/5) can be written as the 5th root of y.
z^(1/4) can be written as the 4th root of z.
Now, let's combine these simplified expressions:
x^(1/6) * y^(1/5) * z^(1/4)
= (6th root of x) * (5th root of y) * (4th root of z)
Since these roots have different denominators, we can find a common denominator by multiplying all the denominators together:
6 * 5 * 4 = 120
Now, let's rewrite each root with the common denominator:
= (120th root of x^6) * (120th root of y^5) * (120th root of z^4)
Finally, we can combine these roots into a single radical expression:
= 120th root of (x^6 * y^5 * z^4)
So, x^(1/6) * y^(1/5) * z^(1/4) can be written as the 120th root of (x^6 * y^5 * z^4).