Exponents and Powers Class 7 Worksheet — Free PDF Download with Answers

An interesting thing happens in the first week of teaching exponents. Students love the idea. Writing $2^5$ instead of $2 \times 2 \times 2 \times 2 \times 2$ feels like a cheat code. Then the laws arrive — multiply the same base by adding exponents, divide by subtracting, and so on — and the confusion starts. That is when paper practice earns its keep.

I have watched children master exponents by doing exactly the same kind of drill every day for ten days. The drill is simple: write the rule at the top of the page, then work five questions that use the rule. By the end of the ten days, the rule is in their bones. This kind of spaced repetition works beautifully on paper and is almost impossible to replicate on an app.

Writing exponents by hand also develops something important — accuracy in small things. The $2$ in $x^2$ is a superscript, sitting slightly above the line. It is easy to miss or to write in the wrong place. Exam markers do not give marks for ambiguous notation. Only paper practice teaches the discipline of writing it correctly every time.

Another advantage of worksheets is that they force students to think rather than guess. An app might let a student tap through questions without really understanding. A worksheet, with no hints and no timer pressure, rewards the student who takes a moment to apply the right rule.

And there is the ever important point about screen time. A quiet worksheet session is a gentle break from devices, which every Class 7 student can benefit from.

The worksheet covers every sub topic from the Class 7 Exponents chapter.

Sub topics:

* Writing numbers in exponential form
* Laws of exponents (product, quotient, power of power)
* Exponent with base $10$
* Numbers in standard form (scientific notation)
* Zero exponent
* Expressing large and small numbers

Level breakdown:

Total 60 questions with a full answer key.

Revise these rules before beginning.

* Exponential form — $a^n$ means $a$ multiplied by itself $n$ times. Here $a$ is the base and $n$ is the exponent.
* Product rule — $a^m \times a^n = a^{m+n}$.
* Quotient rule — $a^m \div a^n = a^{m-n}$ (for $m > n$, $a \neq 0$).
* Power of a power — $(a^m)^n = a^{mn}$.
* Power of a product — $(ab)^n = a^n \times b^n$.
* Power of a quotient — $\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$.
* Zero exponent — $a^0 = 1$ for any $a \neq 0$.
* Standard form — A number written as $k \times 10^n$ where $1 \leq k < 10$. Example: $3200 = 3.2 \times 10^3$.

Quick tip: When a problem looks complicated, identify the base first. If the bases are the same, use the product or quotient rule. If the bases are different, simplify each base separately.

Level 1 — Easy

1. Write $3 \times 3 \times 3 \times 3$ in exponential form.
Solution: $3^4$.

2. Find the value of $2^5$.
Solution: $2 \times 2 \times 2 \times 2 \times 2 = 32$.

3. Simplify: $a^3 \times a^2$.
Solution: $a^{3+2} = a^5$.

Level 2 — Medium

1. Simplify: $\dfrac{2^7}{2^4}$.
Solution: $2^{7-4} = 2^3 = 8$.

2. Simplify: $(3^2)^3$.
Solution: $3^{2 \times 3} = 3^6 = 729$.

3. Write $52000$ in standard form.
Solution: $5.2 \times 10^4$.

Level 3 — Hard

1. Simplify: $\dfrac{2^5 \times 3^4}{2^3 \times 3^2}$.
Solution: $2^{5-3} \times 3^{4-2} = 2^2 \times 3^2 = 4 \times 9 = 36$.

2. Find the value of $x$ if $2^x = 64$.
Solution: $64 = 2^6$, so $x = 6$.

3. Express the distance from Earth to the Sun, $149{,}600{,}000$ km, in standard form.
Solution: $1.496 \times 10^8$ km.

1. Print — A4 paper works best.
2. Warm up — Write all eight laws of exponents at the top of your notebook from memory.
3. Time yourself — 15 minutes for Level 1, 25 for Level 2, 35 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redo every wrong question with the rule named in the margin.
6. Try again — Retry wrong questions the next day.

Daily plan: 20 to 25 minutes per day for two weeks.

Weekly revision: Every Sunday, pick ten questions from the full sheet and solve without looking at the rules. If you get stuck, you need more rule practice.

1. Adding bases instead of multiplying — Students sometimes calculate $2^3 \times 2^2$ as $4^5$. The correct approach is $2^{3+2} = 2^5 = 32$.

2. Multiplying exponents when adding — Writing $2^3 + 2^2 = 2^5$. Addition does not follow the product rule. $2^3 + 2^2 = 8 + 4 = 12$.

3. Wrong sign in quotient rule — For $\dfrac{a^5}{a^2}$, subtracting gives $a^3$, not $a^7$.

4. Forgetting zero exponent rule — $7^0 = 1$, not $0$ and not $7$.

5. Standard form errors — The first number must be between $1$ and $10$. Writing $52 \times 10^3$ is wrong; it should be $5.2 \times 10^4$.

6. Ignoring negative bases — $(-3)^2 = 9$, but $-3^2$ often means $-(3^2) = -9$. Brackets matter.

CBSE (NCERT)
Exponents and Powers is Chapter 13 of NCERT Class 7 maths. Weightage is around 8 to 10 marks. Questions focus on the rules and standard form.

ICSE (Selina / ML Aggarwal)
ICSE covers exponents in depth with more multi step simplification. Weightage is around 10 to 12 marks. Students must show each rule they apply.

IB MYP
IB MYP introduces exponents through patterns. Students notice that repeated multiplication can be written in a shorthand form, and then derive the laws through investigation.

Download the free Class 7 Exponents and Powers worksheet:

* Exponents ICSE Worksheet
* Exponents and Powers IB Worksheet

Online practice:

* Exponents Online — ICSE
* Exponents and Powers Online — IB

* AI Maths Solver — Upload any exponent problem for a step by step solution.
* Spark Coach — AI tutor for guided learning.
* Class 7 Maths Complete Guide
* All Worksheets Hub
* Class 7 Formulas

Week 1: Rules mastery

* Day 1: Read the chapter and list all eight laws.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 questions 1 to 10.
* Day 5: Level 2 questions 11 to 20.
* Day 6: Redo wrong answers.
* Day 7: Rest.

Week 2: Applications and standard form

* Day 8: Level 3 questions 1 to 10.
* Day 9: Level 3 questions 11 to 20.
* Day 10: Redo wrong Level 3 answers.
* Day 11: Standard form drill — 10 large and 10 small numbers.
* Day 12: Mixed quiz.
* Day 13: Mock test (45 minutes).
* Day 14: Review.

* Class 7 Algebraic Expressions Worksheet
* Class 7 Integers Worksheet
* Class 7 Rational Numbers Worksheet
* Class 7 Simple Equations Worksheet
* Class 7 Maths Complete Guide