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The value of (36)1/6 is:
36
1
2
(6)1/3
(6)1/3
Express 36 as 62, then apply the exponent rule (am)n=am×n to multiply the powers: 2×61=31.
The expression given is (36)1/6.
(am)n=am×n
Express 36 as 62, then apply the exponent rule (am)n=am×n to multiply the powers: 2×61=31.
Students might incorrectly calculate 361/6 as 36=6 or forget to simplify the fraction 62 to 31.
Step 1: Express the base in exponential form
Write the number 36 in terms of its prime power or a power of 6, since 36=62.
36=62
Step 2: Substitute into the original expression
Substitute 62 for 36 in the expression (36)1/6.
(62)1/6
Step 3: Apply the power of a power rule
Use the rule of exponents (am)n=am×n to multiply the exponents 2 and 61.
62×61=662=631
D is correct because simplifying (36)1/6 yields (62)1/6=62/6=61/3, which matches Option D.
Questions involving fractional exponents frequently appear in surds and indices problems in competitive exams. Always look to reduce the base to a prime or common factor to simplify indices.
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