In Exercises $$ 7-21 $$, simplify the expression. Write your answer using only positive exponents. $$ \begin{array}{lll} ext { 7. } \frac{7^{-2} m^{0}}{n^{-4}} & ext { 8. } \frac{(-9)^{0} j^{-1} k^{-4}}{2^{0}} & ext { 9. } \frac{5^{-2} w^{0}}{y^{-10}} \ \begin{array}{lll} ext { 10. } \frac{t^{-5}}{8^{-2} s^{-3}} & ext { 11. } \frac{3^{-2} a^{-1}}{9^{-1} b^{-2} c^{0}} & ext { 12. } \frac{17 x^{0} y^{-8}}{4^{-2} z^{-6}} \ ext { 13. }\left(p^{6} ight)^{3} & ext { 14. }\left(q^{-4} ight)^{5} & ext { 15. } 5^{3} \cdot 5^{-7} \ ext { 16. }-4 \bullet(-4)^{-2} & ext { 17. } \frac{x^{7}}{x^{4}} \cdot x^{2} & ext { 18. } \frac{v^{5} \cdot v^{3}}{v^{2}}\end{array} \ ext { 19. }\left(-8 t^{2} ight)^{3} & ext { 20. }\left(\frac{q^{4}}{5} ight)^{-3} & ext { 21. }\left(\frac{1}{3 h^{5}} ight)^{-4}\end{array} $$

Question

In Exercises $$ 7-21 $$, simplify the expression. Write your answer using only positive exponents. $$ \begin{array}{lll}	ext { 7. } \frac{7^{-2} m^{0}}{n^{-4}} & 	ext { 8. } \frac{(-9)^{0} j^{-1} k^{-4}}{2^{0}} & 	ext { 9. } \frac{5^{-2} w^{0}}{y^{-10}} \ \begin{array}{lll}	ext { 10. } \frac{t^{-5}}{8^{-2} s^{-3}} & 	ext { 11. } \frac{3^{-2} a^{-1}}{9^{-1} b^{-2} c^{0}} & 	ext { 12. } \frac{17 x^{0} y^{-8}}{4^{-2} z^{-6}} \ 	ext { 13. }\left(p^{6}ight)^{3} & 	ext { 14. }\left(q^{-4}ight)^{5} & 	ext { 15. } 5^{3} \cdot 5^{-7} \ 	ext { 16. }-4 \bullet(-4)^{-2} & 	ext { 17. } \frac{x^{7}}{x^{4}} \cdot x^{2} & 	ext { 18. } \frac{v^{5} \cdot v^{3}}{v^{2}}\end{array} \ 	ext { 19. }\left(-8 t^{2}ight)^{3} & 	ext { 20. }\left(\frac{q^{4}}{5}ight)^{-3} & 	ext { 21. }\left(\frac{1}{3 h^{5}}ight)^{-4}\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's simplify each of the expressions from Exercises **7** to **21**, ensuring that all exponents are positive.

---

### **7.** $$\dfrac{7^{-2} m^{0}}{n^{-4}}$$

**Simplification:**
$$
\frac{7^{-2} \cdot m^{0}}{n^{-4}} = \frac{7^{-2} \cdot 1}{n^{-4}} = 7^{-2} \cdot n^{4} = \frac{n^{4}}{7^{2}} = \frac{n^{4}}{49}
$$

**Answer:** $$\boxed{\dfrac{n^{4}}{49}}$$

---

### **8.** $$\dfrac{(-9)^{0} j^{-1} k^{-4}}{2^{0}}$$

**Simplification:**
$$
\frac{(-9)^0 \cdot j^{-1} \cdot k^{-4}}{2^0} = \frac{1 \cdot j^{-1} \cdot k^{-4}}{1} = \frac{1}{j \cdot k^{4}}
$$

**Answer:** $$\boxed{\dfrac{1}{j k^{4}}}$$

---

### **9.** $$\dfrac{5^{-2} w^{0}}{y^{-10}}$$

**Simplification:**
$$
\frac{5^{-2} \cdot w^{0}}{y^{-10}} = \frac{5^{-2} \cdot 1}{y^{-10}} = 5^{-2} \cdot y^{10} = \frac{y^{10}}{5^{2}} = \frac{y^{10}}{25}
$$

**Answer:** $$\boxed{\dfrac{y^{10}}{25}}$$

---

### **10.** $$\dfrac{t^{-5}}{8^{-2} s^{-3}}$$

**Simplification:**
$$
\frac{t^{-5}}{8^{-2} \cdot s^{-3}} = t^{-5} \cdot 8^{2} \cdot s^{3} = 64 \cdot s^{3} \cdot t^{-5} = \frac{64 s^{3}}{t^{5}}
$$

**Answer:** $$\boxed{\dfrac{64 s^{3}}{t^{5}}}$$

---

### **11.** $$\dfrac{3^{-2} a^{-1}}{9^{-1} b^{-2} c^{0}}$$

**Simplification:**
$$
\frac{3^{-2} \cdot a^{-1}}{9^{-1} \cdot b^{-2} \cdot c^{0}} = \frac{3^{-2} \cdot a^{-1}}{9^{-1} \cdot b^{-2} \cdot 1} = 3^{-2} \cdot a^{-1} \cdot 9^{1} \cdot b^{2}
$$
$$
= 3^{-2} \cdot 3^{2} \cdot a^{-1} \cdot b^{2} = 3^{0} \cdot \frac{b^{2}}{a} = \frac{b^{2}}{a}
$$

**Answer:** $$\boxed{\dfrac{b^{2}}{a}}$$

---

### **12.** $$\dfrac{17 x^{0} y^{-8}}{4^{-2} z^{-6}}$$

**Simplification:**
$$
\frac{17 \cdot x^{0} \cdot y^{-8}}{4^{-2} \cdot z^{-6}} = \frac{17 \cdot 1 \cdot y^{-8}}{4^{-2} \cdot z^{-6}} = 17 \cdot y^{-8} \cdot 4^{2} \cdot z^{6}
$$
$$
= 17 \cdot 16 \cdot z^{6} \cdot y^{-8} = 272 \cdot \frac{z^{6}}{y^{8}} = \frac{272 z^{6}}{y^{8}}
$$

**Answer:** $$\boxed{\dfrac{272 z^{6}}{y^{8}}}$$

---

### **13.** $$\left(p^{6}\right)^{3}$$

**Simplification:**
$$
\left(p^{6}\right)^{3} = p^{6 \times 3} = p^{18}
$$

**Answer:** $$\boxed{p^{18}}$$

---

### **14.** $$\left(q^{-4}\right)^{5}$$

**Simplification:**
$$
\left(q^{-4}\right)^{5} = q^{-4 \times 5} = q^{-20} = \frac{1}{q^{20}}
$$

**Answer:** $$\boxed{\dfrac{1}{q^{20}}}$$

---

### **15.** $$5^{3} \cdot 5^{-7}$$

**Simplification:**
$$
5^{3} \cdot 5^{-7} = 5^{3 + (-7)} = 5^{-4} = \frac{1}{5^{4}} = \frac{1}{625}
$$

**Answer:** $$\boxed{\dfrac{1}{625}}$$

---

### **16.** $$-4 \cdot (-4)^{-2}$$

**Simplification:**
$$
-4 \cdot (-4)^{-2} = (-4)^{1} \cdot (-4)^{-2} = (-4)^{1 + (-2)} = (-4)^{-1} = \frac{1}{-4} = -\frac{1}{4}
$$

**Answer:** $$\boxed{-\dfrac{1}{4}}$$

---

### **17.** $$\dfrac{x^{7}}{x^{4}} \cdot x^{2}$$

**Simplification:**
$$
\frac{x^{7}}{x^{4}} \cdot x^{2} = x^{7-4} \cdot x^{2} = x^{3} \cdot x^{2} = x^{3+2} = x^{5}
$$

**Answer:** $$\boxed{x^{5}}$$

---

### **18.** $$\dfrac{v^{5} \cdot v^{3}}{v^{2}}$$

**Simplification:**
$$
\frac{v^{5} \cdot v^{3}}{v^{2}} = \frac{v^{5+3}}{v^{2}} = \frac{v^{8}}{v^{2}} = v^{8-2} = v^{6}
$$

**Answer:** $$\boxed{v^{6}}$$

---

### **19.** $$\left(-8 t^{2}\right)^{3}$$

**Simplification:**
$$
\left(-8 t^{2}\right)^{3} = (-8)^{3} \cdot \left(t^{2}\right)^{3} = -512 \cdot t^{6} = -512 t^{6}
$$

**Answer:** $$\boxed{-512 t^{6}}$$

---

### **20.** $$\left(\dfrac{q^{4}}{5}\right)^{-3}$$

**Simplification:**
$$
\left(\dfrac{q^{4}}{5}\right)^{-3} = \left(\dfrac{5}{q^{4}}\right)^{3} = \dfrac{5^{3}}{q^{12}} = \dfrac{125}{q^{12}}
$$

**Answer:** $$\boxed{\dfrac{125}{q^{12}}}$$

---

### **21.** $$\left(\dfrac{1}{3 h^{5}}\right)^{-4}$$

**Simplification:**
$$
\left(\dfrac{1}{3 h^{5}}\right)^{-4} = (3 h^{5})^{4} = 3^{4} \cdot \left(h^{5}\right)^{4} = 81 \cdot h^{20} = 81 h^{20}
$$

**Answer:** $$\boxed{81 h^{20}}$$

---

All expressions have been simplified with only positive exponents as required.
Here are the simplified expressions for Exercises 7-21: 7. $$\dfrac{n^{4}}{49}$$ 8. $$\dfrac{1}{j k^{4}}$$ 9. $$\dfrac{y^{10}}{25}$$ 10. $$\dfrac{64 s^{3}}{t^{5}}$$ 11. $$\dfrac{b^{2}}{a}$$ 12. $$\dfrac{272 z^{6}}{y^{8}}$$ 13. $$p^{18}$$ 14. $$\dfrac{1}{q^{20}}$$ 15. $$\dfrac{1}{625}$$ 16. $$-\dfrac{1}{4}$$ 17. $$x^{5}$$ 18. $$v^{6}$$ 19. $$-512 t^{6}$$ 20. $$\dfrac{125}{q^{12}}$$ 21. $$81 h^{20}$$ **Summary of Simplifications:** - **Exercises 7-21** have been simplified to expressions with only positive exponents.

In Exercises , simplify the expression. Write your answer using only positive
exponents.

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In Exercises , simplify the expression. Write your answer using only positive exponents.