Unit Test (Solutions): Power Play | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each

Q1. Which of the following is equal to 2³ × 2⁴?   (1 Mark)
a) 2⁷
b) 2¹²
c) 2⁸¹
d) 2¹

Answer: a) 2⁷

Same base → add exponents → 2³ × 2⁴ = 2³⁺⁴ = 2⁷

Q2. The value of (3⁴) ÷ (3²) is:   (1 Mark)
a) 3⁸
b) 3²
c) 3⁶
d) 3¹

Answer: b) 3²

Same base → subtract exponents → 3⁴ ÷ 3² = 3⁴⁻² = 3²

Q3. Which of the following is NOT correct?   (1 Mark)
a) a^m × aⁿ = a^m+n
b) (a^m)ⁿ = a^mn
c) a^m ÷ aⁿ  = a^m+n
d) a⁰ = 1

Answer: c) a^m ÷ aⁿ  = a^m+n

The rule is a^m ÷ aⁿ  = a^m-n, not m+n

Q4. The value of 2⁻³ is:   (1 Mark)
a) -8
b) 8
c) 1/8
d) 1/-8

Answer: c) 1/8

Negative exponent rule → a⁻ⁿ = 1/aⁿ

Q5. If 5ˣ = 125, then the value of x is:   (1 Mark)
a) 2
b) 3
c) 4
d) 5

Answer: b) 3

125 = 5³, so on comparing powers  x = 3.

Q6: Express 4^-3 as a power with base 2. (2 Marks)

Solution:

4^-3 can be written as:

4^-3 = (2²)^-3

Now, by using exponential law i.e. (a^m)ⁿ = a^mn

4^-3 = 2^-6 (which is in base 2 form).

Q7: Express 0.00000000837 in standard form. (2 Marks)

Solution:

0.00000000837

= 0.00000000837 x 10⁹ / 10⁹

= 8.37 ×10^-9

Q8: Simplify the expression: (4² × 4⁻³). (2 Marks)

Solution: Using the product rule aᵐ × aⁿ = aᵐ⁺ⁿ

Now, by applying the rule in given expression 4² × 4⁻³ we get,
= 4²⁺⁽⁻³⁾
= 4⁻¹

Now the outcome is in the form of negative exponent rule a⁻ⁿ = 1/aⁿ.
∴ 4⁻¹ = 1/4¹

Therefore, the simplified expression is 1/4

Q9: Solve (3 Marks)

Solution:
Given:On solving:

Q10: Find value of  (3 Marks)

Solution: (i)

(ii)

Q11: Express the following numbers in standard form. (3 Marks)
(i) 0.0000000015
(ii) 0.00000001425
(iii) 102000000000000000

Solution: 
(i) 0.0000000015 = 1.5 ×10^-9
(ii) 0.00000001425 = 1.425×10^-8
(iii) 102000000000000000 = 1.02×10¹⁷

Q12: Simplify the following   (5 Marks)

Solution: 

Q13: The number of books in a library increases by 5 times every 2 years. A library starts with 100 books. How many books will there be in the library after:

(a) 6 years

(b) 10 years

Solution:  Initial number of books = 100

The number of books increases by a factor of 5 every 2 years.

(a) After 6 years (3 periods of 2 years):

Number of books after 6 years = 100 × 5³ = 100 × 125 = 12500 books

• After 6 years: 12500 books

(b) After 10 years (5 periods of 2 years):

Number of books after 10 years = 100 × 5⁵ = 100 × 3125 = 312500 books

• After 10 years: 312500 books