Question

3. Solve the following questions. Each question carries 2 marks.
(8 marks)
a) Express 351 as a product of powers of its prime factors.
b) The mean of 10 observations was calculated as 40. On rechecking, it was
detected that the number 45 was incorrectly copied as 15. Find the correct mean.
c) Simplify and express the following in exponential form:
54 x xloys
54 x x
d) Simplify 43 x 23 x 503​

Answer 1

Given : number 351

The mean of 10 observations was calculated as 40. On rechecking, it was

detected that the number 45 was incorrectly copied as 15.

To Find : Express 351 as a product of powers of its prime factors.

Correct Mean

Solution:

351  = 3 * 117

=> 351  = 3 * 3 * 39

=> 351  = 3 * 3 * 3 * 13

=> 351 = 3³ × 13

The mean of 10 observations was calculated as 40

=> calculated total = 10 * 40 = 400

number 45 was incorrectly copied as 15.

Correct  total = 400 - 15 + 45 = 430

Correct  Mean = 430 / 10  = 43

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