When the following fraction is reduced, what will be the exponent on the m? 27mn^3/51m^6n

6
5
3
4

1 answer

To simplify the fraction \(\frac{27mn^3}{51m^6n}\), we start by simplifying the coefficients and then the variables.

First, let's simplify the coefficients:

\[ \frac{27}{51} = \frac{27 \div 3}{51 \div 3} = \frac{9}{17} \]

Next, we simplify the variables:

For \(m\): \[ \frac{m}{m^6} = m^{1-6} = m^{-5} \]

For \(n\): \[ \frac{n^3}{n} = n^{3-1} = n^{2} \]

Combining these results, we have:

\[ \frac{27mn^3}{51m^6n} = \frac{9}{17} m^{-5} n^{2} \]

Now we express the fraction as:

\[ \frac{9n^{2}}{17m^{5}} \]

Thus, when the fraction is reduced, the exponent on \(m\) is \(5\).

So, the answer is \(\boxed{5}\).