Express using radical notation: sqrt(6ab)^4/3 is the answer ab3sqrt6ab?
To express sqrt(6ab)^4/3 in radical notation, we need to simplify the expression. Let's break it down step by step:
1. First, we can simplify the exponent 4/3. We know that (a^m)^n = a^(m*n). Applying this rule, we have:
(sqrt(6ab))^4/3 = sqrt((6ab)^4/3)
2. Now, let's simplify (6ab)^4/3. We know that (a^m)^n = a^(m*n). So, we can rewrite (6ab)^4/3 as (6ab)^(4/3).
3. To express (6ab)^(4/3) in radical notation, we convert the exponent to a radical. The general rule is a^(m/n) = nth root of (a^m).
In this case, (6ab)^(4/3) can be written as the cube root (because the exponent is 3) of (6ab)^4.
Thus, (6ab)^(4/3) = root(3, (6ab)^4)
4. Expanding further, we have:
root(3, (6ab)^4) = root(3, (6^4)(a^4)(b^4))
(using the rule (ab)^n = a^n*b^n)
5. Finally, simplifying the expression inside the cube root, we have:
root(3, (6^4)(a^4)(b^4)) = root(3, 1296a^4b^4)
So, the answer to sqrt(6ab)^4/3 expressed in radical notation is root(3, 1296a^4b^4).