Math Skill: Roots Of Exponential Expressions
View Lesson | View Sample Problems | Do Worksheet

Instructional videos are displayed with permission from Khan Academy.

Roots Of Exponential Expressions

In this topic, we will be working with radicals (also called roots).

Finding the root of an expression is the opposite of finding the power. We use the radical sign    to show we are looking for roots.

 a1 / n = n  a = b means bn = a

When there is no n, it automatically means 2 or square root.

 a = 2  a
Here is the rule for exponents and powers.
 x ( p / q ) = q  xp

Example 1: Numbers

Find the value of the given expression
 7  321 =

Use the rule for exponents and roots to solve.

 7  321 = (321)( 1/7 ) = 3( 21/7 ) = 33 = 27

Example 2: Variables

Simplify the given expression. Use '^' to indicate 'to the power of' and omit any 1's as coefficients in front of variable expressions.
 56x18 =

Use the rule for exponents and roots to solve in the same way as you would with numbers.

 56x18 = (56x18)( 1/2 ) = (56)( 1/2 ) × (x18)( 1/2 ) = 5(6/2) × x(18/2) = 53x9 = 125x9

### Complexity=5, Mode=exponent

Find the exponent.
1.
 5  2 20
= 2
2.
 3  3 9
= 3

### Complexity=8, Mode=value

Find the value of the given expression.
1.
 5  4 20
=
2.
 5  2 10
=

### Complexity=8, Mode=variable

Simplify the given expression. Use '^' to indicate 'to the power of' and omit any 1's as coefficients in front of variable expressions.
1.
 7 6x 6
=
2.
 3  5 6x 9
=

### Complexity=5, Mode=exponent

Find the exponent.
1
 5  2 20
= 2
Solution
 5  2 20
= (220) (1/5) = 2(20 * 1/5) = 2( 20/5) = 24
2
 3  3 9
= 3
Solution
 3  3 9
= (39) (1/3) = 3(9 * 1/3) = 3( 9/3) = 33

### Complexity=8, Mode=value

Find the value of the given expression.
1
 5  4 20
=
Solution
 5  4 20
= (420) (1/5) = 4(20 * 1/5) = 4( 20/5) = 44 = 256
2
 5  2 10
=
Solution
 5  2 10
= (210) (1/5) = 2(10 * 1/5) = 2( 10/5) = 22 = 4

### Complexity=8, Mode=variable

Simplify the given expression. Use '^' to indicate 'to the power of' and omit any 1's as coefficients in front of variable expressions.