Let a, b, m and n be natural numbers such that $$a1$$ and $$b1$$. If $$a^{m}b^{n}=144^{145}$$, then th

Question

Let a, b, m and n be natural numbers such that $$a>1$$ and $$b>1$$. If $$a^{m}b^{n}=144^{145}$$, then the largest possible value of $$n-m$$ is

Accepted Answer

579. It is given that a m ⋅ b n = 144 145 a^m\cdot b^n\ =\ 144^{145} a m ⋅ b n = 14 4 145 , where a&gt;1\ and b&gt;1 . 144 144 144 can be written as 144 = 2 4 × 3 2 144\ =\ 2^4	imes\ 3^2 144 = 2 4 × 3 2 Hence, a m ⋅ b n = 144 145 a^m\cdot b^n\ =\ 144^{145} a m ⋅ b n = 14 4 145 can be written as

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$ . If $a^{m}b^{n}=144^{145}$ , then the largest possible value of $n-m$ is

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$ . If $a^{m}b^{n}=144^{145}$ , then the largest possible value of $n-m$ is

Let a, b, m and n be natural numbers such that a&gt;1 and b&gt;1. If ambn=144145a^{m}b^{n}=144^{145}ambn=144145, then the largest possible value of n−mn-mn−m is

Let a, b, m and n be natural numbers such that a&gt;1 and b&gt;1. If ambn=144145a^{m}b^{n}=144^{145}ambn=144145, then the largest possible value of n−mn-mn−m is

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$ . If $a^{m}b^{n}=144^{145}$ , then the largest possible value of $n-m$ is

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$ . If $a^{m}b^{n}=144^{145}$ , then the largest possible value of $n-m$ is