The product Cube root of 2 . Fourth root of 2 . Twelfth root of 32 is equal to..
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It is given that ,
product of cube root of 2 , fourth
root of 2 and twelfth root of 32
= 2^1/3 × 2^1/4 × 32^12
= 2^1/3 × 2^1/4 × ( 2^5 )^12
= 2^1/3 × 2^1/4 × 2^5/12
= 2^(1/3+1/4+5/12)
[ We know exponential rule <,
a^m × a^n = a^m+n ]
= 2^ [ (4 + 3 + 5 )/12 ]
= 2^(12/12)
= 2¹
= 2
••••
product of cube root of 2 , fourth
root of 2 and twelfth root of 32
= 2^1/3 × 2^1/4 × 32^12
= 2^1/3 × 2^1/4 × ( 2^5 )^12
= 2^1/3 × 2^1/4 × 2^5/12
= 2^(1/3+1/4+5/12)
[ We know exponential rule <,
a^m × a^n = a^m+n ]
= 2^ [ (4 + 3 + 5 )/12 ]
= 2^(12/12)
= 2¹
= 2
••••
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44
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