Fractional Exponents - Discovery Education

SD School Pre-Algebra
Program 3: Roots and Rational Numbers
QuikNotes
A cube root like a square root, except the number is
multiplied 3 times to get another whole number. The
cube root of 729 equals 9, because 9 x 9 x 9 = 729.
Student Notes
The 3 in the arm of the radical signals to us that we’re
looking for the cube root.
3
729 = 9
Whenever we have a cube root, or some other odd root,
it’s possible for us to end up with a negative number
under the radical. This is because whenever we multiply
an odd number of negative integers together, our
answer will be negative.
3
−8 =−2 because (−2) × (−2) × (−2) =−8
If there is a negative number under the radical and
we’re looking for an even root, like the square root of
negative 4, it is undefined. The reason we say it’s
undefined is because we can’t find one real number
multiplied by itself to equal negative 16.
This is different than when we have a negative sign in
front of our radical. Remember that this means we’re
looking for the negative of the square root of a number,
which we can do for any number. So, here the negative
square root of 16 is -4.
− 16 =−4
−16 is undefined
Raising a number to the fourth power means
multiplying that number four times. So, the fourth root
of a number means finding the number that when
multiplied 4 times gives us our original number.
For example:
4
16 = 2 because 2 × 2 ×2 × 2 = 16
When we’ve got a number with an exponent that’s a
simple fraction, like 3 to the one-half power, it just
means the square root of 3. We look at what number is
in the denominator and take that root of our base
number.
1
3 2
= 3