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

May 18, 2017

Any negative exponent will make the number become its reciprocal.

If the negative number is in the numerator, then it will go to the denominator, and if it is in the denominator then it will go to the numerator.

Like so

${b}^{3} \cdot \left({m}^{-} 3\right) \cdot \left({b}^{-} 6\right)$

$= {b}^{3} \cdot \frac{1}{m} ^ 3 \cdot \frac{1}{b} ^ 6$

$= {\cancel{b}}^{3} \cdot \frac{1}{m} ^ 3 \cdot \frac{1}{{\cancel{b}}^{6} {b}^{3}}$

$= \frac{1}{{m}^{3} {b}^{3}}$

May 18, 2017

$\frac{1}{{b}^{3} {m}^{3}}$

#### Explanation:

Exponent rules can be tricky to figure out at first. Fortunately, these are quite simple.

In the problem you have, you need to at least know both the Negative Exponent Rule and the Product Rule.

The Negative Exponent Rule states:

${x}^{-} n = \frac{1}{x} ^ n$

The Product Rule states:

${x}^{a} \cdot {x}^{b} = {x}^{a + b}$

So, if you have ${b}^{3} \left({m}^{-} 3\right) \left({b}^{-} 6\right)$, then you know you have two terms for which you can use the Product Rule. We'll use that on the $b$ terms.

Like so: ${b}^{3 - 6} \cdot {m}^{-} 3 = {b}^{-} 3 \cdot {m}^{-} 3$

Now, since $b$ and $m$ are different variables, they cannot combine in the Product Rule. Therefore, the only thing left to do is use the Negative Exponent Rule. As displayed in the example above, just move the two terms to the denominator and make the exponents positive, making sure to leave a $1$ in the numerator.

$\frac{1}{{b}^{3} {m}^{3}}$