Let us look at a few examples of expressions that include rational exponents. 
The expressions could contain both negative and fractional exponents.

Let's first deal with the negative exponent before rewriting the expression as a radical.
Recall that negative exponents indicate that you need to take the reciprocal of the base.

Then we will rewrite the expression so that there are no fractional exponents.
The fractional exponent indicates that the base is inside a radical.

 

Click here for the first example

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
 
 
 
 
 















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64 raised to the negative three halves power
 
 
 
 
 


What is the base?













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64 raised to the negative three halves power
 
 
 
 
 


What is the base? 64

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64 raised to the negative three halves power
 
 
 
 
 


What is the base? 64
What is the exponent?












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64 raised to the negative three halves power
 
 
 
 
 


What is the base? 64
What is the exponent? -3/2

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64 raised to the negative three halves power
 
 
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression?

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64 raised to the negative three halves power
 
 
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent

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64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
 
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
 
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
 
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index?









Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
 
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written?







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64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of one-sixty-fourth, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of one-sixty-fourth, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written?






Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of one-sixty-fourth, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of one-sixty-fourth, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate?





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64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
 
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.

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64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base?



Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base? 1/8

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base? 1/8
What is the exponent?


Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base? 1/8
What is the exponent? 3

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
 


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base? 1/8
What is the exponent? 3
Evaluate the expression.

Click here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 raised to the negative three halves power
one-sixty-fourth raised to the three halves power
square root of one-sixty-fourth, all to the third power
square root of 1/8 times 1/8, all to the third power
1/8 raised to the third power
1 over 512


What is the base? 64
What is the exponent? -3/2
How should you rewrite the expression? without negative exponent
Only take the reciprocal of the base.
Rewrite the expression without the fractional exponent.
What is the index? 2
Does the 2 have to be written? no
Why does the 2 not have to be written? square root has index 2
What does this index indicate? find the base that was multiplied to itself 2 times.
Evaluate the radical.
What is the base? 1/8
What is the exponent? 3
Evaluate the expression.

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