SIMPLIFYING RADICAL AND RATIONAL EXPONENTS

To simplify radical with rational exponents, we have to follow the procedure given below.

Radicals can be converted into exponents

If we see the composite number inside the radical, we can write it in exponential form by decomposing it into prime factors.
Incase of finding more than one power, we can multiply the powers using the rules of exponents.

Evaluate the expression without a calculator. Simplify completely.

Problem 1 :

Solution :

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

So, the answer is 27.

Problem 2 :

Solution :

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

So, the answer is 1/100000.

Problem 3 :

Solution :

So, the answer is 9.

Problem 4 :

Solution :

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

So, the answer is 1/2.

Problem 5 :

Solution :

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

So, the answer is -1/64.

Problem 6 :

Solution :

So, the answer is √2.

Problem 7 :

Solution :

So, the answer is 1/8.

Problem 8 :

Solution :

So, the answer is -32.

Problem 9 :

(a) 12 (b) 9² (c) 81⁴ (d) 27^3/4

Solution :

So, option (b) is correct.

Problem 10 :

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.

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