Rational Exponent

How to solve and use a rational exponent: formula, 5 examples, and their solutions.

Formula

Formula

nam = am/n

Example 1

Example

Solution

16 = 24

Power

324 = 24/3

So 24/3 is the answer.

Example 2

Example

Solution

a7/9 = 9a7

So 9a7 is the answer.

Example 3

Example

Solution

45/2
= (22)5/2
= 22⋅[5/2]

Power of a Power

2⋅[5/2] = 5

25 = 32

So 32 is the answer.

Example 4

Example

Solution

3-7/2⋅35/2 = 3-7/2 + 5/2

Product of Powers

-7/2 + 5/2 = -2/2

-2/2 = -1

So 1/3 is the answer.

Example 5

Example

Solution

Change each radical
to a rational exponent power.

3x2 = x2/3

6x
= 6x1
= x1/6

x
= 2x1
= x1/2

So
[3x26x]/√x
= [x2/3⋅x1/6]/x1/2.

[x2/3⋅x1/6]/x1/2
= x2/3 + 1/6 - 1/2

Change the denominators to 6.

[2/3]⋅[2/2] = 4/6
-[1/2]⋅[3/3] = -3/6

4/6 + 1/6 - 3/6
= 5/6 - 3/6
= 2/6

2/6 = 1/3

x1/3
= 3x1
= 3x

So 3x is the answer.