# EVALUATING RATIONAL EXPONENTS WITHOUT CALCULATOR

By understanding the rules given below, we can evaluate the rational exponents simply.

To evaluate rational exponents without help of calculator, we may have to follow the steps given below.

Step 1 :

Write the numerals that we have inside the parenthesis in exponential form using prime factorization.

Step 2 :

If there are more than one term inside the parenthesis, we have to combine them using the rules of exponents.

Step 3 :

Incase we have negative exponent, change it as positive by taking the reciprocal.

Step 4 :

After the simplification done, incase we have power, we may have to evaluate it.

Problem 1 :

Solution :

By decomposing 100, we get 10 x 10

100 = 102

Problem 2 :

Solution :

Problem 3 :

Solution :

Problem 4 :

Solution :

By decomposing 25, we get 5 x 5

25 = 52

Problem 5 :

Solution :

By decomposing 8, we get 2 x 2 x 2

8 = 23

Problem 6 :

Solution :

64 can be written as 8 x 8 (or) 2 x 2 x 2 x 2 x 2 (or) 4 x 4 x 4

Here considering the denominator of the rational exponent it is 3, based on this we decide to decompose 64 as product of three same numbers.

64 = 43

Problem 7 :

Solution :

64 can be written as 8 x 8 (or) 2 x 2 x 2 x 2 x 2 (or) 4 x 4 x 4

Here considering the denominator of the rational exponent it is 2, based on this we decide to decompose 64 as product of three same numbers.

64 = 82

Problem 8 :

Solution :

Problem 9 :

Solution :

Problem 10 :

Solution :

Problem 11 :

Solution :

Problem 12 :

Solution :

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