use rational exponents to write
x 1/4.y 1/6.z 1/9
as a single radical expression
you could write it as
x^(9/36) y^(6/36) z^(4/36)
= (x^9 y^6 z^4)^(1/36)
or 36th root of (x^9 y^6 z^4)
To write the expression using rational exponents as a single radical expression, you need to find a common denominator for the exponents of each variable x, y, and z.
The common denominator for the exponents 1/4, 1/6, and 1/9 is 36.
Now, rewrite each exponent with the common denominator:
x^(1/4) = x^(9/36)
y^(1/6) = y^(6/36)
z^(1/9) = z^(4/36)
Next, use the rule that states if you have a product of exponential expressions with the same base, you can combine the exponents by adding them together.
Therefore, the expression becomes:
x^(9/36).y^(6/36).z^(4/36)
To simplify this further, let's rewrite it using a single radical expression:
(x^(9/36) . y^(6/36) . z^(4/36))^(36/36)
Since any number raised to the power of 1 is itself, we can simplify the exponent to:
(x^(9/36) . y^(6/36) . z^(4/36))^1
Finally, our single radical expression is:
∛(x^9 . y^6 . z^4)