Question

If m and n are whole numbers such that mn = 169, then the value of (m – 1) n + 1 is:
a) 1
b) 13
c) 169
d) 1728​

Answer 1

Given:

m and n are whole numbers such that mn= 169.

To Find:

The value of (m – 1) n + 1.

Solution:

To find the value of (m – 1) n + 1 we will follow the following steps:

We have given that

${m}^{n} = 169$

As we know,

The Square of 13 is 169.

So,

${13}^{2} = 169$

The value of m and n is equal to 13 and 2 respectively.

${(m - 1)}^{n + 1} = {(13 - 1)}^{2 + 1}$

${(m - 1)}^{n + 1} = {(12)}^{3}$

The cube of 12 Is equal to 1728.

So,

${(m - 1)}^{n + 1} =1728$

Henceforth, the value of (m – 1) n + 1 is d) 1728.