If 2724^6 = 14^m+ 14^n, what is the value of mn?

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PS · Problem Solving

705-805

Divisibility/Multiples/Factors

If $\frac{272}{4^6} = \frac{1}{4^m}+ \frac{1}{4^n}$ , what is the value of $mn$ ?

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A

2

B

4

C

6

8

Correct

E

12

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Official Explanation

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\frac{272}{4^6} =\frac{4*68}{4^6}=\frac{68}{4^5}=\frac{4+64}{4^5}=\frac{4}{4^5} +\frac{4^3}{4^5}=\frac{1}{4^4}+\frac{1}{4^2}=\frac{1}{4^m}+ \frac{1}{4^n}

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If $\frac{272}{4^6} = \frac{1}{4^m}+ \frac{1}{4^n}$ , what is the value of $mn$ ?

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If 27246=14m+14n\frac{272}{4^6} = \frac{1}{4^m}+ \frac{1}{4^n}46272​=4m1​+4n1​, what is the value of mnmnmn?

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If $\frac{272}{4^6} = \frac{1}{4^m}+ \frac{1}{4^n}$ , what is the value of $mn$ ?