Re-write with a rational exponent and simplify.
^3 sqrt:22
3sqrt22 = 3(22)^(1/2).
To rewrite the expression ^3 sqrt(22) with a rational exponent, we need to express the square root as a fractional exponent. Recall that the square root of a number could be written as the number raised to the power of 1/2.
Therefore, we have:
^3 sqrt(22) = (22)^(1/2)^3
Next, we simplify the expression by applying the exponent power to both the numerator and the denominator. In this case, the exponent power of 3 is applied to both the numerator and the denominator.
So, the expression becomes:
^3 sqrt(22) = (22)^(1/2 * 3)
Simplifying the exponent, we have:
^3 sqrt(22) = (22)^(3/2)
Therefore, ^3 sqrt(22) can be rewritten with a rational exponent as (22)^(3/2).