# How do you simplify (m^-3)(-2m^-5)(-m^6)?

Jun 3, 2015

First start by moving the ( ${m}^{-} 3$) and (${m}^{-} 5$) to the denominator in order to make the exponents positive. By doing this, you should get $\left(\frac{\left(- {m}^{6}\right) \left(- 2\right)}{\left({m}^{3}\right) \left({m}^{5}\right)}\right)$.

Now you can multiply the two terms in the numerator. You do so in two steps:
1. multiply the coefficients $\left(- 1\right) \left(- 2\right)$ and
2. keep the ${m}^{6}$
This should give you the term $- 2 {m}^{6}$. The whole fraction should look like $\left(\frac{2 {m}^{6}}{\left({m}^{3}\right) \left({m}^{5}\right)}\right)$.

Now you can multiply the two terms in the denominator. You do so in three steps:
1. multiply the coefficients $\left(1\right) \left(1\right)$,
2. keep the base $\left(m\right)$, and
3. add the exponents $3 + 5$.
This is based off the rule ${x}^{a} \cdot {x}^{b} = {x}^{a + b}$. This should give you the term ${m}^{8}$. The whole fraction should look like $\left(\frac{2 {m}^{6}}{{m}^{8}}\right)$.

Now you can divide the two terms. You do so in three steps:
1. divide the coefficients $2 / 1$,
2. keep the base $\left(m\right)$, and
3. subtract the exponents $6 - 8$.
This is based off of the rule ${x}^{a} / {x}^{b} = {x}^{a - b}$. This should give you the term ${m}^{-} 2$.

Once again, to make the exponent positive, you have to move it to the denominator. this should give you $\left(\frac{2}{{m}^{2}}\right)$.

Hope this helped!! :)