If r > 0 and r^4= 27, the r^6= ?
To find the value of r^6, we need to use the given information r > 0 and r^4 = 27.
First, let's find the value of r. We know that r^4 = 27, so we can take the fourth root of both sides of the equation to obtain r:
√(r^4) = √27
r = √(27) = ±√(3^3) = ±3√3
Note that we only take the positive root because it's mentioned that r > 0.
Now that we have the value of r, we can substitute it into the expression r^6:
(r^6) = (±3√3)^6
To simplify this equation, we raise ±3√3 to the power of 6:
(r^6) = (±3√3)^6 = (±3^6)(√3^6)
Simplifying further:
(r^6) = (±729)(3^3)
(r^6) = ±729 * 27
Now we can evaluate the expression:
(r^6) = ±19683
Therefore, r^6 could be either positive or negative 19683.