PROPERTIES OF RATIONAL EXPONENTS AND RADICALS

Evaluate the following :

Problem 1 :

Solution :

When we have two or more terms with the same base and they are multiplied, we have to put only one base and add the powers.

Problem 2 :

Solution :

When we have power raised by another power, we have to multiply both the powers.

Problem 3 :

Solution :

Step 1 :

Inside the parenthesis, we have composite numbers. We write these numbers in exponential form.

Step 2 :

Instead of using same powers for both, we can put only one power for all the bases which are multiplied.

Step 3 :

When we have power raised by another power, we have to multiply the powers.

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :

Problem 7 :

Solution :

Problem 8 :

Solution :

Problem 9 :

Solution :

Problem 10 :

Solution :

Evaluate the expression without a calculator. Simplify completely.

Problem 11 :

Solution :

By writing 81 in exponential form, we get 81 = 3⁴.

So, the answer is 27.

Problem 12 :

Solution :

By writing 100 in exponential form, we get 100 = 10².

So, the answer is 1/100000.

Problem 13 :

Solution :

So, the answer is 9.

Problem 14 :

Solution :

By writing 16 in exponential form, we get 16 = 2⁴.

So, the answer is 1/2.

Problem 15 :

Solution :

By writing 256 in exponential form, we get 256 = 4⁴.

So, the answer is -1/64.

Problem 16 :

Solution :

So, the answer is √2.

Problem 17 :

Solution :

So, the answer is 1/8.

Problem 18 :

Solution :

So, the answer is -32.

Problem 19 :

(a)  12  (b)  9²   (c)  81⁴   (d)  27^3/4

Solution :

So, option (b) is correct.

Problem 20 :

Solution :

So, option (a) is correct. 

Problem 11 :

(a)  -6x⁴√5  (b)  -6x⁸√5   (c)  6x⁴i√5  (d)  6x⁸i√5

Solution :

So, option (d) is correct.