# Simplify [(-9)^17 (-9)^0]/[(-9)^14 (-9)] - [(5^14)^6]/[(5^4)^20 * 5]

#### lotus

##### New member
Simplify Completely:

$$\displaystyle \dfrac{(-9)^{17}\, (-9)^0}{(-9)^{14}\, (-9)}\, -\, \dfrac{(5^{14})^6}{(5^4)^{20}\, \cdot\, 5}\, =\, ?$$

$$\displaystyle \dfrac{(-9)^{17}\, (1)}{(-9)^{14}\, (-9)}\, -\, \dfrac{(5^{14 \cdot 6})}{(5^{4\cdot 20})\, \cdot\, 5}$$

$$\displaystyle \dfrac{-9^{17}}{-9^{14}}\, -\, \dfrac{5^{84}}{5^{80}\, \cdot \, 5}$$

Confused as to what to do next.

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#### MarkFL

##### Super Moderator
Staff member
Well, for starters, you have to be careful, as in general:

$$\displaystyle (-a)^b\ne -a^b$$

The original expression $$\displaystyle E$$ is:

$$\displaystyle \displaystyle E=\frac{(-9)^{17}(-9)^{0}}{(-9)^{14}(-9)}-\frac{\left(5^{14}\right)^6}{\left(5^{4}\right)^{20}\cdot5}$$

Using the rules:

$$\displaystyle a^ba^c=a^{b+c}$$

$$\displaystyle \left(a^b\right)^c=a^{bc}$$

We have:

$$\displaystyle \displaystyle E=\frac{(-9)^{17}}{(-9)^{15}}-\frac{5^{84}}{5^{81}}$$

Now, use the rule:

$$\displaystyle \displaystyle \frac{a^b}{a^c}=a^{b-c}$$

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