Question

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

6
5
3
4

Answer 1

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 \(\boxed{5}\).