 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=c5
(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=5cbz3
(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 =55pqmn2
(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= 230b2c2

(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=280m2n3

II. Convert each of the following exponential form to (expanded) product form:
(i) y3z2
(ii) p2q3r5
(iii) 5khb2
(iv) 18c3d4h5
(v) 25ab2cd3

Solution:

(i) y3z2
y3 is written in expanded form as y × y × y.
z2 is written in expanded form as z × z.
y3z2= y × y × y × z × z.
(ii) p2q3r5
p2 is written in expanded form as p × p.
q3 is written in expanded form as q × q × q.
r5 is written in expanded form as r × r × r × r × r.
p2q3r5= p × p × q × q × q × r × r × r × r × r.
(iii) 5khb2
b2 is written in expanded form as b × b.
5,h,k is written only once.
5khb2= 5 × k ×h × b × b.
(iv) 18c3d4h5
c3 is written in expanded form as c × c × c.
d4 is written in expanded form as d × d × d × d.
h5 is written in expanded form as h × h × h × h × h.
18c3d4h5=18 × c × c × c × d × d × d × d × h × h × h × h × h.
(v) 25ab2cd3
25, a, c are written once.
b2 is written in expanded form as b × b.
d3 is written in expanded form as d × d × d.
25ab2cd3=25 × a × b × b × c × d × d × d.

III. Write each of the following in product form:
(i) 3p2q4r
(ii) 73b4c2z3
(iii) a4b3c2
(iv) 7p2q3r4
(v) 17ac2dy3

Solution:

(i) Given 3p2q4r
p2=p × p
q4=q × q × q × q
3p2q4r is written in product form as 3 × p × p × q × q × q × q × r.

(ii) Given 73b4c2z3
b4= b × b × b × b
c2= c × c
z3= z × z × z
73b4c2z3 is written in product form as 73 × b × b × b × b × c × c × z × z × z.
(iii) Given a4b3c2
a4= a × a × a × a
b3= b × b × b
c2 = c × c
a4b3c2 is written in product form as a × a × a × a × b × b × b × c × c
(iv)Given 7p2q3r4
p2= p × p
q3= q × q × q
r4= r × r × r × r
7p2q3r4 is written in product form as 7 × p × p × q × q × q × r × r × r × r.
(v) Given 17ac2dy3
c2= c × c
y3= y × y × y
17ac2dy3=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=p4
a was written 2 times. It can be written as an exponent of 2.
a × a=a2
b was written 3 times. It can be written as an exponent of 3.
b × b × b=b3
p × p × p × p x a × a × b × b × b in exponential form is p4a2b3.
(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=a2
b was written 3 times. It can be written as an exponent of 3.
b × b × b=b3
10 × a × a × b × b × b × c=10a2b3c.
(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=c8
d was written 8 times. It can be written as an exponent of 8.
d × d × d × d × ..… 8 times=d8
c × c × c × c × ..… 8 times d × d × d × d × ..… 8 times=c8d8.
(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=a10.
b was written 7 times. It can be written as an exponent of 7.
b × b × b × ..… 7 times=b7.
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=a10b7c14.
(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=a6
b was written 3 times. It can be written as an exponent of 3.
b × b × b=b3
5 × a × a × a ×…6 times b × b × b=5a6b3

V. State whether true or false:
(i) m × m × m × m × m × m = m6
(ii) 5 × 2 × a × a × b × b = 52a2b2
(iii) 3 × 7 × b × b × c × c × c = 33b2c3
(iv) k × l × k × l × k × l = k3l3
(v) m × n × 10 × p × q × q× p = 10mnp2q2
(vi) a × a × a × b × b × b × c × c=a3b3c2
(vii) 6 × a × a × b × b × b × c × c=6a2b3c2

Solution:

(i) true
(ii) false
(iii) false
(iv) true
(v) true
(vi) true
(vii) true