Tricky Exponents!!

importance of prime numbers
The ‘Prime’ Importance of Prime Numbers
March 13, 2016
Integrated reasoning
Integrated Reasoning
May 23, 2016
Exponents in exams

In some previous articles we have learnt about a few interesting concepts on exponents. In this piece of articulation let us enjoy some exam focused properties of the tricky exponent!

23 = 2 x 2  x 2

But this could also be written as 23 = 22 x 2;  also, multiplication is addition that many number of times. Eg: 2 x 3 = 2 + 2 + 2.

Likewise, for the first equation, we can write, 23 = 22 + 22.

In order to generalise it, 35 = 34 x 3, or 34 + 34 + 34 or

57= 56 x 5 = 56 + 56 +56 +56 +56

This property is extensively used in standardised tests:

  1. If, 2m + 2n  = 240 find the value of (m + n) , where, m & n are integers.
  2. 40
  3. 60
  4. 78
  5. 80
  6. 158

Solution:

Using the same property, we have 2m + 2n = 240 = 239 x 239.

This is the only combination whose sum will give 240.

Thus, m & n = 39

m + n  = 39 + 39 = 78

Answer: C

  1. If, 3x x 3y x 3z = 312, where x, y & z are integers. Find the highest prime factor of xyz.
  2. 3
  3. 5
  4. 11
  5. 13
  6. 127

Solution:

Same logic, so, 312 = 311 + 311 + 311 ;

Thus, possible values for x,y & z = 11, 11 and 11.

xyz = 11 x 11 x 11 = 113

The highest prime factor of  is 113 is 11.

Answer: C

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