Please solve it..........
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Lets take term by term:
root(3*5^-3) = 3^(1/2) * 5^(-3/2)
cuberoot(3^-1) = 3^(-1/3)
root5 = 5^1/2
6th root(3*5^6) = 3^1/6 * 5^6/6 = 3^1/6 * 5
Now the question looks like:
(3^1/2 * 5^(-3/2) ) /( 3^(-1/3) * 5^1/2) ) * (3^1/6 * 5)
= 3^(1/2 + 1/3 + 1/6) * 5^(-3/2 - 1/2 + 1)
= 3^(3+2+1/6) * 5^(-4/2 + 1)
= 3^(6/6) * 5^(-2+1) = 3^1*5^-1
= 3/5
Hence proved.
Hope it helps.
[concepts: a^m* a^n = a^(m+n)... a^-m = 1/a^m]
root(3*5^-3) = 3^(1/2) * 5^(-3/2)
cuberoot(3^-1) = 3^(-1/3)
root5 = 5^1/2
6th root(3*5^6) = 3^1/6 * 5^6/6 = 3^1/6 * 5
Now the question looks like:
(3^1/2 * 5^(-3/2) ) /( 3^(-1/3) * 5^1/2) ) * (3^1/6 * 5)
= 3^(1/2 + 1/3 + 1/6) * 5^(-3/2 - 1/2 + 1)
= 3^(3+2+1/6) * 5^(-4/2 + 1)
= 3^(6/6) * 5^(-2+1) = 3^1*5^-1
= 3/5
Hence proved.
Hope it helps.
[concepts: a^m* a^n = a^(m+n)... a^-m = 1/a^m]
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