DAV Class 6 Maths Chapter 6 Worksheet 3 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 6 Worksheet 3 Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 6 WS 3 Solutions

Question 1.
Write the exponential form of:

(a) (y) × (y) × (y) × (y) × ………….. 9 times
Solution:
y⁹

(b) p × p × p × …………. 21 times
Solution:
p²¹

(c) \(\frac{1}{2}\) × a × b × b × c
Solution:
\(\frac{1}{2}\) ab²c

(d) 2 × a × a × a × b × b × c
Solution:
2a³b²c

(e) – 6 × (x) × (y) × (y) × (z)
Solution:
– 6xy²z

(f) (- z) × (- z) × (- z) × (- z)
Solution:
(- z)⁴

(g) (- a) × (- a) × (- a) × (- a) × ………… 17 times
Solution:
(- a)¹⁷

(h) (3x) × (3x) × (3x) × (3x) × (3x)
Solution:
(3x)⁵

Question 2.
Write the product form of the following:

(a) y⁵
Solution:
y⁵ = y × y × y × y × y

(b) x¹⁹
Solution:
x¹⁹ = x × x × x × x × x ……….. × 19 times

(c) \(\frac{3}{4}\) x²yz
Solution:
\(\frac{3}{4}\) x²yz = \(\frac{3}{4}\) x × x × y × z

(d) a³b²c
Solution:
a³b²c = a × a × a × b × b × c

(e) (- a)⁴
Solution:
(- a)⁴ = (- a) × (- a) × (- a) × (- a)

(f) (2x)³
Solution:
(2x)³ = 2x × 2x × 2x

(g) (- z)³⁰
Solution:
(- z)³⁰ = (- z) × (- z) × (- z) × (- z) × (- z) …………. 30 times

(h) – 7pq²r³
Solution:
– 7pq²r³ = – 7 × p × q × q × r

Question 3.
Write the product form of (3x)³ and 3x³. Are they same?
Solution:
(3x)³ = 3x × 3x × 3x = 27x³
= 3 × x × x × x = 3x³
27x³ ≠ 3x³
Hence (3x)³ and 3x³ are not same.

Question 4.
Write the coefficient of:

(a) x in 2x
Solution:
Coefficient of x in 2x = 2

(b) a in – 9a
Solution:
Coefficient of a in – 9a = – 9

(c) y in 4xy
Solution:
Coefficient of y in 4xy = 4x

(d) b in – 8abc
Solution:
Coefficient of b in – 8abc = – 8ac

(e) a in – a
Solution:
Coefficient of a in – a = – 1

(f) z in \(\frac{3}{4}\) z
Solution:
Coefficient of z in \(\frac{3}{4}\) z = \(\frac{3}{4}\)

(g) x² in 4x²y
Solution:
Coefficient of x² in 4x²y = 4y

(h) y in y
Solution:
Coefficient of y in y = 1

(i) a in – \(\frac{1}{2}\) ab²
Solution:
Coefficient of a in – \(\frac{1}{2}\) ab² = – \(\frac{1}{2}\) b²

(j) z in zy
Solution:
Coefficient of z in zy = y

Question 5.
Identify the following statements as constants or variables:

(a) Number of mangoes in one dozen mangoes
Solution:
Constant

(b) Number of centimetres in a metre
Solution:
Constant

(c) Temperature in a day
Solution:
Variable

(d) Degrees in a right angle
Solution:
Constant

(e) Degrees in an acute angle
Solution:
Variable

(f) Number of days in February
Solution:
Variable

(g) Number of days in April
Solution:
Constant

(h) Number of letters in the word MATHEMATICS.
Solution:
Constant

Question 6.
Write the numerical coefficient in:

(a) 2x
Solution:
2

(b) 3yz
Solution:
3

(c) \(\frac{1}{4}\) x²z
Solution:
\(\frac{1}{4}\)

(d) a
Solution:
1

(e) – yz
Solution:
– 1

(f) 3pqr
Solution:
3

(g) \(\frac{4}{3}\) a²bc
Solution:
\(\frac{4}{3}\)

(h) x²yz
Solution:
1

(j) – bc
Solution:
– 1

(j) – x
Solution:
– 1