# How do you evaluate the expression ((-4)^2(-4)^-3)/((-4)^-5) using the properties?

Mar 28, 2017

$256.$

#### Explanation:

Recall that, $\frac{{a}^{l} \cdot {a}^{m}}{a} ^ n = {a}^{l + m - n} .$

Accordingly, the Exp.$= {\left(- 4\right)}^{2 + \left(- 3\right) - \left(- 5\right)} .$

$= {\left(- 4\right)}^{2 - 3 + 5} = {\left(- 4\right)}^{4} = 256.$

Mar 28, 2017

${\left(- 4\right)}^{4} \mathmr{and} 256$

#### Explanation:

It is my believe that you are familiar with the properties. We will use the ff for this questions. Feel free to ask if you don't know all the properties yet.

${\left(x\right)}^{3} \cdot {\left(x\right)}^{2} = {\left(x\right)}^{3 + 2} = {\left(x\right)}^{5}$

${\left(x\right)}^{3} / {\left(x\right)}^{2} = {\left(x\right)}^{3 - 2} = x$

Now let's move on to the question

$\frac{{\left(- 4\right)}^{2} {\left(- 4\right)}^{-} 3}{- 4} ^ - 5$

First, simplify the numerator. Since they both have the same bases, we simply add the exponents because they are multiplying.

$\frac{{\left(- 4\right)}^{2 + \left(- 3\right)}}{- 4} ^ - 5$

$\frac{{\left(- 4\right)}^{2 - 3}}{- 4} ^ - 5$

$\frac{{\left(- 4\right)}^{-} 1}{- 4} ^ - 5$

Now to division, you can simply change the sign of the exponent when you bring it to the numerator. Let me show you how.

The property says we should subtract the exponent of the denominator from that of the numerator provided they have the same bases.

${\left(- 4\right)}^{- 1 - \left(- 5\right)}$

${\left(- 4\right)}^{- 1 + 5}$

${\left(- 4\right)}^{4}$

$256$

Note: When a negative base is raised to an even exponent, the answer is positive. When a negative base is raised to an odd exponent, the answer is negative.