# Tricky Exponents!!

March 13, 2016
###### Integrated Reasoning
May 23, 2016

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

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.

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