Math Skill: Roots Of Exponential Expressions
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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

The answer is  


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

The answer is

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
 =  

Answers

Complexity=5, Mode=exponent

Find the exponent.
#Correct AnswerYour Answer
1
5  2 20
 = 2
Solution
5  2 20
= (220) (1/5) = 2(20 * 1/5) = 2( 20/5) = 24
#Correct AnswerYour Answer
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.
#Correct AnswerYour Answer
1
5  4 20
 =  
Solution
5  4 20
= (420) (1/5) = 4(20 * 1/5) = 4( 20/5) = 44 = 256
#Correct AnswerYour Answer
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.
#Correct AnswerYour Answer
1
   7 6x 6
 =  
Solution
   7 6x 6
= (7 6x 6)(1/2) = 7(6 * 1/2) x(6 * 1/2) = 7(6/2) x(6/2) = 73x3 = 343x 3
#Correct AnswerYour Answer
2
3  5 6x 9
 =  
Solution
3  5 6x 9
= (5 6x 9)(1/3) = 5(6 * 1/3) x(9 * 1/3) = 5(6/3) x(9/3) = 52x3 = 25x 3
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