Index Notation: Problem Solving & Reasoning

Mathematics
Grade 7
18 questions
~36 mins
1 views0 downloads

About This Worksheet

This worksheet explores the use of index notation in prime factorization, including procedural practice, problem solving, and real-world applications. Designed for Grade 7 students to develop understanding and reasoning skills.

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Index Notation: Problem Solving & Reasoning

Subject: MathematicsGrade: Grade 7
Name:
Date:
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Untitled Worksheet

Grade Grade 7
A

Fluency & Practice

Answer the following questions to practice basic skills with index notation and prime factorization. Show your working in the grid spaces provided.
1.
Express 64 as a power of 2 using index notation.
[1 mark]
2.
Write the prime factorization of 150 in exponential form.
[2 marks]
3.
Simplify the expression: 3^4 × 3^2 using index notation.
[2 marks]
4.
If a number is written as 2^3 × 2^4, what is its value in index notation?
[1 mark]
B

Targeted Practice

Solve these questions to deepen your understanding of index notation and prime factorization.
1.
Express 210 as a product of primes in exponential form.
[2 marks]
2.
Write 81 as a power of 3 using index notation.
[1 mark]
3.
Calculate the value of 2^3 × 2^5 using index notation.
[2 marks]
4.
Simplify the expression: 5^2 × 5^3.
[2 marks]
5.
Express 360 in prime factors using index notation.
[2 marks]
C

Problem Solving & Reasoning

Answer the following multi-step problems, explaining your reasoning clearly.
1.
Given that 2^a × 3^b = 72, find the values of a and b. Explain how you used index notation to find your answer.
[3 marks]
2.
The prime factorization of a number is 2^4 × 5^2. What is the number? Show your working using index notation.
[3 marks]
3.
If a number equals 2^x × 7^y and its value is 448, find x and y. Use index notation in your explanation.
[3 marks]
D

Real-world Applications

Apply your understanding of index notation in these real-world scenarios.
1.
A factory produces 2^5 items per day. Express the total items produced in 10 days using index notation.
[2 marks]
2.
A device uses 3^3 units of energy daily. Write an expression, in index notation, for the total energy used in 7 days.
[2 marks]
E

Challenge & Extension

Attempt these advanced problems to further develop your skills with index notation.
1.
Express 1024 as a power of 2 and explain why this is a correct use of index notation.
[2 marks]
2.
The number 630, when expressed as a product of primes, is 2 × 3^2 × 5. Rewrite this in index notation and verify its value.
[3 marks]
F

Mixed Review & Error Analysis

Review the common mistakes in index notation. Identify and correct the errors in the following problems.
1.
A student writes 2^3 + 2^4 = 2^7. Is this correct? Explain your reasoning and correct if necessary.
[3 marks]
2.
Express 81 as 3^3. Is this correct? If not, correct the expression.
[2 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet