If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?

Question

If  \frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36} , what is the value of n ?

A. -1
B. 0
C. 1
D. 2
E. 3

Luckisnoexcuse · Answer

2^{(-n-1)} * 3^{(-n-1)} = 2^{-2} * 3^{-2}

-n-1 =-2 
 -n=-1 
 n=1

C

sashiim20 · Answer

\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}

\frac{1}{3*2^n}*\frac{1}{2*3^n} = \frac{1}{2^2*3^2}

\frac{1}{3*2^n*2*3^n} = \frac{1}{2^2*3^2}

\frac{1}{2^{(n+1)}*3^{(n+1)}} = \frac{1}{2^2*3^2}

2^{(n+1)} = 2^2

n + 1 = 2   => n = 2-1 = 1

3^{(n+1)} = 3^2

n + 1 = 2   => n = 2-1 = 1

Therefore  n = 1

Answer (C)...

rulingbear · Answer

By just dropping the numerators down. We see that we get the 1/ (36)^(n)^2 = 1/36, n=1. C

TheMechanic · Answer

We need 36 in denominator of LHS such that it equals the RHS. It can be only gotten when the value of n = 1. Hence C.

generis · Answer

\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}

\frac{1}{2^{n}3^{1}}*\frac{1}{3^{n}2^{1}} = \frac{1}{6^{2}}

Different base, same exponent rule:  a^{n}*b^{n} = (ab)^{n} . Combine  2^{n}  *  3^{n}  (= 6^{n} ), as well as  2^1  *  3^1  (= 6^1 )

\frac{1}{6^{n}6^{1}} = \frac{1}{6^{2}}

\frac{6^{(-n)}}{6^{1}} = 6^{(-2)}

6^{(-n-1)} = 6^{(-2)}

-n - 1 = -2 
 n = 1

Answer C

BrentGMATPrepNow · Answer

Given:  \frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2}=\frac{1}{36}

On the left side of this equation, let's multiply the numerators together, and then we'll multiply the denominators.

NUMERATORS : 
 2^{-n}  x  3^{-n}  =  6^{-n}

DENOMINATORS : 
3 x 2 = 6

So, when we simplify the left side of the equation, we get:  \frac{6^{(-n)}}{6} = \frac{1}{36}

From here, we can multiply both sides by 6 to get:  6^{(-n)} = \frac{1}{6}

Next, recognize that  \frac{1}{6} = 6^{(-1)}

So, we can write:  6^{(-n)} = 6^{(-1)}

From this, we can conclude that -n = -1, which means n = 1

RELATED VIDEO
 https://www.youtube.com/watch?v=EVUOYdRgt30

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If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?

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If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?

Prep Toolkit

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My Rewards