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Which of the following is the value of the expression $913 × 27 − 12 316 × 3 − 23$ ?

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313

3 − 1 3

3 − 1 6

3 − 1 6

answer is B.

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Detailed Solution

The given expression is,

913 × 27 − 12 316 × 3 − 23

Write 9 as

32

and 27 as

33

in a given fraction.
Apply the following identity:
(

a m) n = a m n

∴ 913 × 27 − 12 316 × 3 − 23 = 3 2 × 13 × 3 − 3 × 12 316 × 3 − 2 3

Apply the following identity:

a m ⋅ a n = a m + n

⇒ 913 × 27 − 12 316 × 3 − 23 = 3 − 5 6 3 − 1 2

Apply the following identity:

a m a n = a m − n, m > n

⇒ 913 × 27 − 12 316 × 3 − 23 = 3 − 1 3

Therefore, the value of the given expression

913 × 27 − 1 2 316 × 3 − 2 3 = 3 − 1 3 .

Hence, option (2) is correct.

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