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
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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]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet