Question

Find the value of m and n, if $6^{-5}\times 5^{-2}\times 6^3\times 5^m\times 6^n=1$. [4 MARKS]

Answer 1

Steps: 2 Marks
Application: 1 Mark
Answer: 1 Mark

$6^{-5}\times 5^{-2}\times 6^3\times 5^m\times 6^n=1$

$6^{-5}\times 6^3\times 6^n\times 5^{-2}\times 5^m=1$

$6^{-5+3+n}\times 5^{-2+m}=1$

$6^{-2+n}\times 5^{-2+m}=1$

The bases of both the numbers are not equal.

So, the value will be equal to 1, when the exponents of these bases will be equal to zero.

Any non - zero number raised to the power zero is 1.

So, the exponents of both 6 and 5 are zero.

Therefore,

$-2+m=0\Rightarrow m=2$

$-2+n=0\Rightarrow n=2$

$\therefore m=n$