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 = 10^{2}
Problem 2 :
Solution :
Problem 3 :
Solution :
Problem 4 :
Solution :
By decomposing 25, we get 5 x 5
25 = 5^{2}
Problem 5 :
Solution :
By decomposing 8, we get 2 x 2 x 2
8 = 2^{3}
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 = 4^{3}
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 = 8^{2}
Problem 8 :
Solution :
Problem 9 :
Solution :
Problem 10 :
Solution :
Problem 11 :
Solution :
Problem 12 :
Solution :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM