![]() y, to identify the y 2 as a candidate for release.The x 2 term already has an exponent of 2, but you should rewrite the y 3 term as y 2 ![]() The coefficient 18 only has one factor that's a perfect square: 9 so, rewrite 18 as the product 2 Solution: Since this is a square root, you want as much of the radicand as possible to be raised to the second power.It might help to think of ( y 2) 3 as a group of three y 2's, and ( y 2) 3 = y 6 thanks to exponential Rule 3 from Encountering Expressions. Why do you rewrite y 6 as ( y 2) 3 in Example 1(a)? Basically, you're trying to make groups of three things, so that they can be released from the radical. Yank them out in front of the radical, stripping away the third power as they exit the prison, which leaves only 2 and x inside. Of all the pieces in the radicand, only 2 3, x 3, and ( y 2) 3 contain powers of 3.Luckily, y 6 is a perfect cube, since y 2 = y 6, so write it as with that all-important power of 3 as well: ( y 2) 3. x = x 3 + 1 = x 4 so it contains an exponent of 3. ![]()
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