Question

# Write the following numbers in the form of rational indices. (i) Cube root of 8th power of 548 (ii) Square of 3rd root of 131

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Solution

## It is known that, (a)mn=(am)1n mean ′nth root of mth power of a'. (a)mn=(a1n)m means ′mth power of nth root of a'. (i) Cube root of 8th power of 548 =⎧⎪⎨⎪⎩(5488)13⎫⎪⎬⎪⎭=(548)83 (ii) Square of 3 rd root of 131 =⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩⎛⎜ ⎜⎝131⎛⎝13⎞⎠⎞⎟ ⎟⎠2⎫⎪ ⎪ ⎪⎬⎪ ⎪ ⎪⎭=(131)23

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