Question

$6^{-5}$ x $5^{-2}$ x $6^3$ x $5^m$ x $6^n$ = 1, then m + n will be

• A. 4
• B. -4
• C. 3
• D. 2

Answer 1

The correct option is A

4

$6^{-5}$ x $5^{-2}$ x $6^3$ x $5^m$ x $6^n$ = $6^{-5}$ x $6^3$ x $6^n$ x $5^{-2})$ x $5^m$ = $6^{-5+3+n}$ x $5^{-2+m}$ = 1

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

Any number raised to zero is 1.

Then, the exponents of both 6 and 5 are zero.
Therefore,
-2 + m = 0, m = 2
-2 + n = 0, n = 2

m + n = 2 + 2 = 4