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Power of a Product & Quotient

Total questions: 14

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

Simplify the expression.  
 (20)3(13)3\left(20\right)^3\cdot\left(13\right)^3   

a)

 2606260^6  

b)

 26012260^{12}  

c)

 2609260^9  

d)

 2603260^3  

2.

Simplify the expression. 

Choose all the answers that are correct (THERE IS MORE THAN ONE ANSWER!!).



 (1.5)4(5.8)4\left(-1.5\right)^4\cdot\left(5.8\right)^4  

a)

 (8.7)8\left(-8.7\right)^8  

b)

 (8.7)4\left(8.7\right)^4  

c)

 (8.7)4\left(-8.7\right)^4  

d)

 (4.3)4\left(4.3\right)^4  

3.

Simplify the expression. 

 (34)5(49)5\left(\frac{3}{4}\right)^5\cdot\left(\frac{4}{9}\right)^5  

a)

 (13)5\left(\frac{1}{3}\right)^5  

b)

 (1236)25\left(\frac{12}{36}\right)^{25}  

c)

 (13)25\left(\frac{1}{3}\right)^{25}  

d)

 (1236)5\left(\frac{12}{36}\right)^5  

4.

Simplify the expression. 

Choose all the answers that are correct (THERE IS MORE THAN ONE ANSWER!!).

 (58)6(23)6\left(-\frac{5}{8}\right)^6\cdot\left(\frac{2}{3}\right)^6   


a)

 (512)6\left(-\frac{5}{12}\right)^6  

b)

 (512)12\left(-\frac{5}{12}\right)^{12}  

c)

 (512)6\left(\frac{5}{12}\right)^6  

d)

 (1024)6\left(-\frac{10}{24}\right)^6  

5.

Simplify the expression. 

 z9n9z^9\cdot n^9  

a)

 (zn)18\left(zn\right)^{18}  

b)

 zn9zn^9  

c)

 (zn)9\left(zn\right)^9  

d)

 (zn)81\left(zn\right)^{81}  

6.

Simplify the expression. 

 (2k)10(8r)10(5t)10\left(2k\right)^{10}\cdot\left(8r\right)^{10}\cdot\left(5t\right)^{10}  

a)

 (15krt)10\left(15krt\right)^{10}  

b)

 (80krt)30\left(80krt\right)^{30}  

c)

 (80krt)10\left(80krt\right)^{10}  

d)

 80krt1080krt^{10}  

7.

Simplify the expression. 

 (25y2)5(15y8)5\left(\frac{2}{5y^2}\right)^5\cdot\left(15y^8\right)^5  

a)

 (220y10)10\left(\frac{2}{20y^{10}}\right)^{10}  

b)

 (6y6)5\left(6y^6\right)^5  

c)

 (6y10)5\left(6y^{10}\right)^5  

d)

 (110y10)5\left(\frac{1}{10y^{10}}\right)^5  

8.

 (40m2)7(18m)7\left(-40m^2\right)^7\cdot\left(\frac{1}{8m}\right)^7  

a)

 (1320m3)7\left(-\frac{1}{320m^3}\right)^7  

b)

 (40m28m)7\left(\frac{40m^2}{8m}\right)^7  

c)

 (5m)7\left(-5m\right)^7  

d)

 (5m3)7\left(-5m^3\right)^7  

9.

Simplify the expression. 

 9010÷1801090^{10^{ }}\div180^{10}  

a)

 (12)10\left(\frac{1}{2}\right)^{10}  

b)

 (12)20\left(\frac{1}{2}\right)^{20}  

c)

 (90180)10\left(\frac{90}{180}\right)^{10}  

d)

 (90180)100\left(\frac{90}{180}\right)^{100}  

10.

Simplify the expression. 

 (40)22÷(2)22\left(-40\right)^{22}\div\left(-2\right)^{22}  

a)

 204420^{44}  

b)

 (20)44\left(-20\right)^{44}  

c)

 202220^{22}  

d)

 (20)22\left(-20\right)^{22}  

11.

Simplify the expression. 

 r13÷w13r^{13}\div w^{13}  

a)

 (rw)26\left(\frac{r}{w}\right)^{26}  

b)

 (rw)13\left(rw\right)^{13}  

c)

 (rw)26\left(rw\right)^{26}  

d)

 (rw)13\left(\frac{r}{w}\right)^{13}  

12.

Simplify the expression. 

(3t)4÷(4s)4\left(-3t\right)^4\div\left(-4s\right)^4

a)

(34st)4\left(-\frac{3}{4}st\right)^4

b)

(3t4s)4\left(\frac{3t}{4s}\right)^4

c)

(3t4s)8\left(\frac{3t}{4s}\right)^8

d)

(34)16\left(\frac{3}{4}\right)^{16}

13.

Simplify the expression. 

Choose all the answers that are correct (THERE IS MORE THAN ONE ANSWER!!).

 2781124169\frac{2^7\cdot8^{11}\cdot2^4}{16^9}  

a)

 51231512^{31}  

b)

 16216^2  

c)

 211811169\frac{2^{11}\cdot8^{11}}{16^9}  

d)

 282^8  

14.

Simplify the expression.

 (610)29205417\frac{\left(6^{10}\right)^2\cdot9^{20}}{54^{17}}  

a)

 542354^{23}  

b)

 54354^3  

c)

 15205417\frac{15^{20}}{54^{17}}  

d)

 (518)3\left(\frac{5}{18}\right)^3