Are these practice questions for Power Play based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 8 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Power Play free?

Yes. Every chapter includes free practice questions for Class 8 students to get you started.

What types of questions are included?

The practice set for Power Play mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Power Play for full coverage.

How many practice questions are there for Power Play?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Power Play Class 8 Mathematics Practice Questions with Answers

easy

Write the number

0.00000507

in standard form (scientific notation).

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easy

Express the following repeated multiplication in exponential form:

a \times a \times a \times b \times b

.

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easy

Critique the following simplification and provide the correct answer with justification:

3^2 \times 3^5 = 9^7

.

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easy

What is the value of any non-zero number raised to the power of zero? For example, find the value of

15^0

.

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easy

Express

(7^3)^4 \div 7^9

in a single exponential form.

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easy

In the expression

7^4

, identify the base and the exponent.

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easy

Define the exponential form of a number.

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easy

Calculate the value of

(-2)^3 \times (-10)^2

.

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easy

List the first five powers of the number 3, starting from

3^1

.

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easy

Find the numerical value of the following expressions: (i)

2^5

(ii)

(-3)^3

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easy

Explain the meaning of a negative exponent. Use the example

5^{-2}

to illustrate your explanation.

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medium

Design a scenario comparing two salary plans for a new job.

Plan A: A starting salary of ₹20,000 per month, with a fixed raise of ₹1,000 each subsequent month.
Plan B: A starting salary of ₹10,000 per month, but the salary doubles each subsequent month.

(i) Formulate expressions for the salary in the 'n-th' month for both plans. (ii) Evaluate which plan provides a higher salary in the 4th month. (iii) Justify in which month the salary from Plan B first surpasses the salary from Plan A.

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medium

State the law of exponents for multiplying two powers with the same base, i.e., for an expression like

n^a \times n^b

.

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medium

Compare the values of

3^{-4}

and

4^{-3}

. Which number is greater?

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medium

Simplify the following expression and write the answer using a positive exponent:

(\frac{4}{5})^{-3} \times (\frac{8}{5})^{-2}

.

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medium

A radioactive substance has a half-life of 10 years. This means its mass reduces by half every 10 years. If the initial mass of the substance is 640 grams, calculate its mass after 40 years.

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medium

A student claims that for any non-zero numbers

x

and

y

, the expression

(x^{-1} + y^{-1})^{-1}

is equal to

x+y

. Critique this claim by evaluating both expressions for

x=2

and

y=3

.

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medium

Create a word problem that models exponential decay. The scenario should start with an initial quantity of 512 units, which is halved at each stage. The problem must ask for a formula for the quantity remaining after 'n' stages and then ask for the quantity remaining after 6 stages.

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medium

Summarize the rule for dividing powers with the same base. Provide the general formula and explain what it means.

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medium

Solve for the value of

p

in the equation:

9 \times 3^p = (27)^{5}

.

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medium

Describe the process of writing a decimal number in expanded form using powers of 10. Use the number 561.903 as an example to illustrate the steps.

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medium

Explain the difference in meaning between the expressions

4+4+4

and

4^3

.

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medium

Based on the source text, explain the concept of exponential growth using the paper folding example. Summarize how the thickness of the paper changes with each fold, starting with an initial thickness of 0.001 cm.

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medium

Design a method to determine the units digit of

(133)^ {101}

. Justify the steps in your method.

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medium

Justify whether the statement

(a^x)^y = a^{(x^y)}

is 'Always True', 'Sometimes True', or 'Never True' for counting numbers

a, x, y > 1

. Provide examples to support your claim.

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medium

Describe how to write a large number in standard form (scientific notation) and express the number

47,500,000

in this form.

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medium

Justify the rule

x^0 = 1

(for any non-zero number

x

) by using the law of division for exponents,

x^a \div x^b = x^{a-b}

.

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medium

A special type of algae in a pond doubles its area every day. On the first day, it covers 10 square meters. (a) Calculate the area covered by the algae after 5 days. (b) If the pond has a total area of 10240 square meters, on which day will the pond be completely covered? (c) On which day was the pond half-covered?

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medium

The speed of light is approximately

3 \times 10^8

m/s. The average distance between the Earth and Jupiter is

7.8 \times 10^{11}

m. Calculate the time it takes for light to travel from Jupiter to Earth. Express your answer in seconds and in standard form.

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medium

Solve for the value of

k

:

5^k = \frac{1}{125}

.

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medium

Explain how to convert a number from standard form to its usual form. Convert

8.03 \times 10^5

to its usual form.

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hard

Formulate a general expression for any number that is simultaneously a perfect square and a perfect cube. Justify your formulation with an example.

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hard

The mass of the Earth is

5.97 \times 10^{24}

kg and the mass of the Sun is

1.989 \times 10^{30}

kg. (a) Calculate the combined mass of the Earth and the Sun. Express the answer in standard form. (b) Analyze how many times more massive the Sun is than the Earth. Round your answer to three significant figures.

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hard

A student simplified the expression

\frac{2^{-5} \times 15^{-4} \times 27}{6^{-5} \times 10^{-4}}

and got the answer

3^4

. Critique the student's answer by providing a detailed, step-by-step correct simplification.

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hard

Create a problem based on the paper folding experiment. Assume a standard sheet of paper is

0.1

mm thick. The distance to the Moon is approximately

384,000

km.

(i) Formulate an expression for the thickness of the paper after 'n' folds. (ii) The world record for paper folding is 12 times. Evaluate the thickness after 12 folds and express it in meters. (iii) Justify, through calculation, how many folds would be required for the paper's thickness to surpass the distance to the Moon. (Hint:

2^{10} \approx 10^3

)

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hard

The mass of a proton is approximately

1.672 \times 10^{-27}

kg, and the mass of an electron is approximately

9.109 \times 10^{-31}

kg. Evaluate how many times more massive a proton is than an electron. Propose your answer in scientific notation, rounded to one decimal place.

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hard

List and explain three fundamental laws of exponents. For each law, state the general formula and provide one simple numerical example.

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hard

A scientist observes a bacterial culture that triples in population every hour. If the experiment starts with 100 bacteria, formulate a general expression for the population, P, after 't' hours. Then, evaluate approximately how many hours it will take for the population to exceed 10 million (

10^7

).

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hard

A mobile phone company wants to generate unique identification numbers for its phones. Option A: A 7-digit code using digits 0-9. Option B: A 5-character code using the 26 letters of the alphabet (A-Z). Analyze which option provides more unique identification numbers by calculating the total possibilities for each.

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hard

The total number of stars in the observable universe is estimated to be

2 \times 10^{23}

. The human population is about

8 \times 10^9

. A science fiction story proposes a plan to assign a unique star to every human who has ever lived. Historians estimate that the total number of humans who have ever lived is about

1.17 \times 10^{11}

.

(i) Evaluate the ratio of the total number of stars to the total number of humans who have ever lived. (ii) Based on your calculation, critique the feasibility of the story's proposal. Is there a surplus or deficit of stars? (iii) If every star had a planetary system with an average of 5 planets, formulate an expression for the total number of planets in the universe and justify how many planets could be assigned to each human who has ever lived.

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hard

An investment of ₹10,000 is made into two different schemes. Scheme A: The amount grows exponentially, multiplying by a factor of

1.5

every 2 years. Scheme B: The amount grows linearly, with ₹2,500 being added to the principal every 2 years. (a) Calculate the value of the investment in Scheme A after 6 years. (b) Calculate the value of the investment in Scheme B after 6 years. (c) Analyze and determine which scheme provides a better return after 6 years.

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hard

Calculate the value of the expression:

((\frac{1}{4})^{-2} - (\frac{1}{3})^{-3}) \div (\frac{1}{2})^{-4}

.

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hard

Without performing the full calculation, justify which of the two numbers is greater:

A = (100^2)^{10}

or

B = 2^{100}

.

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hard

Simplify the expression:

\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}

.

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hard

Evaluate the expression

\left( \frac{x^a}{x^b} \right)^{a+b} \times \left( \frac{x^b}{x^c} \right)^{b+c} \times \left( \frac{x^c}{x^a} \right)^{c+a}

and justify your final answer.

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Power PlayClass 8 Mathematics Practice Questions