EVALUATING RATIONAL EXPONENTS WITHOUT CALCULATOR

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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 :

EVALUATING RATIONAL EXPONENTS WITHOUT CALCULATOR

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