Powers of Literal Numbers is nothing but the repeated product of a number with itself written in exponential form. Practice using the Worksheet on Powers of Literal Numbers and know the different models of questions framed on the topic. Use the Powers of Literal Numbers Worksheet PDF as a cheat sheet to self-examine your preparation on the concept.

Math Students are advised to solve the questions from the Powers of Literal Numbers Worksheet with Answers to master the concept as well as to enhance their general math skills. You can also check the Solutions for the Problems on Literal Numbers Powers in case of any doubts and learn how to frame quality answers in your exams and thereby score well.

## Free Printable Worksheet on Powers of Literal Numbers

**I. Write each of the following in the exponential form:
**(i) c × c × c × c × c

(ii) 5 × c × b × z × z × z

(iii) m × 12 × n × b × z

(iv) m× n × p × q × n × 55

(v) 230 × b × c × c × b

(vi) m × m × n × n × n × 280

**Solution:**

(i) Given c × c × c × c × c

Here c has written as 5 times.

It can be written as an exponent of 5.

c × c × c × c × c=c^{5}

(ii) Given 5 × c × b × z × z × z

Here 5 is written ‘1’ time.

c has written ‘1’ time.

b has written ‘1’ time.

z has written 3 times.

5 × c × b × z × z × z=5cbz^{3}

(iii) m × 12 × n × b × z

Here m is written ‘1’ time.

12 has written ‘1’ time.

n,b, and Z are written 1 time.

m × 12 × n × b × z=12mnbz

(iv) m× n × p × q × n × 55

Here m is written ‘1’ time.

n has written 2 times.

p,q,55 are written 1 time.

m× n × p × q × n × 55 =55pqmn^{2}

(v) 230 × b × c × c × b

Here 230 is written ‘1’time.

b has written 2 times.

c has written 2 times.

230 × b × c × c × b= 230b^{2}c^{2}

(vi) m × m × n × n × n × 280

Here m is written 2 times.

n has written 3 times.

280 has written ‘1’ time.

m × m × n × n × n × 280=280m^{2}n^{3}

**II. Convert each of the following exponential form to (expanded) product form:
**(i) y

^{3}z

^{2}

(ii) p

^{2}q

^{3}r

^{5}

(iii) 5khb

^{2}

(iv) 18c

^{3}d

^{4}h

^{5}

(v) 25ab

^{2}cd

^{3}

**Solution:**

(i) y^{3}z^{2}

y^{3} is written in expanded form as y × y × y.

z^{2} is written in expanded form as z × z.

y^{3}z^{2}= y × y × y × z × z.

(ii) p^{2}q^{3}r^{5}

p^{2} is written in expanded form as p × p.

q^{3} is written in expanded form as q × q × q.

r^{5} is written in expanded form as r × r × r × r × r.

p^{2}q^{3}r^{5}= p × p × q × q × q × r × r × r × r × r.

(iii) 5khb^{2}

b^{2 } is written in expanded form as b × b.

5,h,k is written only once.

5khb^{2}= 5 × k ×h × b × b.

(iv) 18c^{3}d^{4}h^{5}

c^{3} is written in expanded form as c × c × c.

d^{4} is written in expanded form as d × d × d × d.

h^{5} is written in expanded form as h × h × h × h × h.

18c^{3}d^{4}h^{5}=18 × c × c × c × d × d × d × d × h × h × h × h × h.

(v) 25ab^{2}cd^{3}

25, a, c are written once.

b^{2} is written in expanded form as b × b.

d^{3} is written in expanded form as d × d × d.

25ab^{2}cd^{3}=25 × a × b × b × c × d × d × d.

**III. Write each of the following in product form:
**(i) 3p

^{2}q

^{4}r

(ii) 73b

^{4}c

^{2}z

^{3}

(iii) a

^{4}b

^{3}c

^{2}

(iv) 7p

^{2}q

^{3}r

^{4}

(v) 17ac

^{2}dy

^{3}

**Solution:**

(i) Given 3p^{2}q^{4}r

p^{2}=p × p

q^{4}=q × q × q × q

3p^{2}q^{4}r is written in product form as 3 × p × p × q × q × q × q × r.

(ii) Given 73b^{4}c^{2}z^{3}

b^{4}= b × b × b × b

c^{2}= c × c

z^{3}= z × z × z

73b^{4}c^{2}z^{3} is written in product form as 73 × b × b × b × b × c × c × z × z × z.

(iii) Given a^{4}b^{3}c^{2}

a^{4}= a × a × a × a

b^{3}= b × b × b

c^{2} = c × c

a^{4}b^{3}c^{2} is written in product form as a × a × a × a × b × b × b × c × c

(iv)Given 7p^{2}q^{3}r^{4}

p^{2}= p × p

q^{3}= q × q × q

r^{4}= r × r × r × r

7p^{2}q^{3}r^{4} is written in product form as 7 × p × p × q × q × q × r × r × r × r.

(v) Given 17ac^{2}dy^{3}

c^{2}= c × c

y^{3}= y × y × y

17ac^{2}dy^{3}=17 × a × c × c × d × y × y × y.

**IV. Write each of the following products in index (exponential) form:
**(i) p × p × p × p x a × a × b × b × b

(ii) 10 × a × a × b × b × b × c

(iii) c × c × c × c × ..… 8 times d × d × d × d × ..… 8 times.

(iv) a × a × a × ..… 15 times b × b × b × ..… 7 times c × c × c× ..… 20 times.

(v) 5 × a × a × a ×…6 times b × b × b

**Solution:**

(i) Given p × p × p × p x a × a × b × b × b

Here P is written 4 times. It can be written as an exponent of 4.

p × p × p × p=p^{4}

a was written 2 times. It can be written as an exponent of 2.

a × a=a^{2}

b was written 3 times. It can be written as an exponent of 3.

b × b × b=b^{3}

p × p × p × p x a × a × b × b × b in exponential form is p^{4}a^{2}b^{3}.

(ii) Given 10 × a × a × b × b × b × c

Here a is written 2 times. It can be written as an exponent of 2.

a × a=a^{2
}b was written 3 times. It can be written as an exponent of 3.

b × b × b=b^{3}

10 × a × a × b × b × b × c=10a^{2}b^{3}c.

(iii) Given c × c × c × c × ..… 8 times d × d × d × d × ..… 8 times.

c was written 8 times. It can be written as an exponent of 8.

c × c × c × c × ..… 8 times=c^{8}

d was written 8 times. It can be written as an exponent of 8.

d × d × d × d × ..… 8 times=d^{8}

c × c × c × c × ..… 8 times d × d × d × d × ..… 8 times=c^{8}d^{8}.

(iv) Given a × a × a × ..… 10 times b × b × b × ..… 7 times c × c × c × ..… 14 times.

a was written 10 times. It can be written as an exponent of 10.

a × a × a × ..… 10 times=a^{10}.

b was written 7 times. It can be written as an exponent of 7.

b × b × b × ..… 7 times=b^{7}.

c was written 14 times. It can be written as an exponent of 14.

a × a × a × ..… 10 times b × b × b × ..… 7 times c × c × c × ..… 14 times=a^{10}b^{7}c14.

(v) Given 5 × a × a × a ×…6 times b × b × b

a was written 6 times. It can be written as an exponent of 6.

a × a × a ×…6 times=a^{6}

b was written 3 times. It can be written as an exponent of 3.

b × b × b=b^{3}

5 × a × a × a ×…6 times b × b × b=5a^{6}b^{3}

**V. State whether true or false:
**(i) m × m × m × m × m × m = m6

(ii) 5 × 2 × a × a × b × b = 52a

^{2}b

^{2}

(iii) 3 × 7 × b × b × c × c × c = 33b

^{2}c

^{3}

(iv) k × l × k × l × k × l = k

^{3}l

^{3}

(v) m × n × 10 × p × q × q× p = 10mnp

^{2}q

^{2}

(vi) a × a × a × b × b × b × c × c=a

^{3}b

^{3}c

^{2}

(vii) 6 × a × a × b × b × b × c × c=6a

^{2}b

^{3}c

^{2}

**Solution:**

(i) true

(ii) false

(iii) false

(iv) true

(v) true

(vi) true

(vii) true