Exponents (Negative Exponents)

1. $\dfrac{1}{7^2}$ or $\dfrac{1}{49}$ $$\eqalign{7^{-2}=\dfrac{1}{7^2}=\dfrac{1}{7\cdot7}= \dfrac{1}{49}}$$

2. $\dfrac{1}{(-2)^{5}}$ or $\dfrac{1}{-32}$ $$\eqalign{{(-2)^{-5}}=\dfrac{1}{-2^{-5}}=\dfrac{1}{-2\cdot2\cdot2\cdot2\cdot2}= \dfrac{1}{-32}}$$

3. ${6^3}$ or $216$

4. $3^2$ or $9$   $$\eqalign{(\dfrac{1}{3})^{-2}=\dfrac{1^{-2}}{3^{-2}}=\dfrac{3^2}{1^2}= \dfrac{9}{1} = 9}$$

5. $x^5$

6. $\dfrac{1}{n^3}$ $$\eqalign{n^{-3}}=\dfrac{1}{n^{3}}$$

7. $7^4$ or $2,401$

8. $\dfrac{1}{-6^2}$ or $\dfrac{1}{-36}$ $$\eqalign{{-6^{-2}}=\dfrac{1}{-6^{2}}=\dfrac{1}{-6\cdot6}= \dfrac{1}{-36}}$$ 

(Note: beacaue the problem states $-6^2$ and not $(-6)^2$, only 6 is squared, not -6.  $-6^2$ is equivent to $-1 \times 6 \times 6$, so the answer comes out negative.  $(-6^2)$ would be equivalent to $-6 \times -6$ which is a positive 36.

9. $4^3a^3$ or $64a^3$

10. $3x$

11. $\dfrac{1}{k^{10}}$

12. $\dfrac{t^7}{2^3}$ or $\dfrac{t^7}{8}$