Podcast
Questions and Answers
What is the estimated value of $6.5^{2}$?
What is the estimated value of $6.5^{2}$?
The square root of 14 is closer to 3 than it is to 4.
The square root of 14 is closer to 3 than it is to 4.
False
Estimate the value of $√39$.
Estimate the value of $√39$.
6
The estimated value of $√18.2$ is approximately ____.
The estimated value of $√18.2$ is approximately ____.
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Match the following expressions with their estimated values:
Match the following expressions with their estimated values:
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What is the value of $7^3$?
What is the value of $7^3$?
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The expression $5^{-2}$ equals to $ rac{1}{25}$.
The expression $5^{-2}$ equals to $ rac{1}{25}$.
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What is the product of $4^4$ and $4^2$?
What is the product of $4^4$ and $4^2$?
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The expression $2^{-3}$ can be rewritten as __________.
The expression $2^{-3}$ can be rewritten as __________.
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Match the following powers with their results:
Match the following powers with their results:
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The base can be negative when dealing with powers.
The base can be negative when dealing with powers.
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What is the simplified form of $11^{-4}$?
What is the simplified form of $11^{-4}$?
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$9^{-2} = rac{1}{81}$ is true.
$9^{-2} = rac{1}{81}$ is true.
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What is the result of simplifying $( rac{1}{5^5})^{-1}$?
What is the result of simplifying $( rac{1}{5^5})^{-1}$?
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The expression $2^{3} imes 2^{-2}$ simplifies to $2^{______}$.
The expression $2^{3} imes 2^{-2}$ simplifies to $2^{______}$.
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Which of the following expressions represents a perfect square?
Which of the following expressions represents a perfect square?
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Explain how to simplify $3^0$.
Explain how to simplify $3^0$.
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To simplify $64^{-1/2}$, the result is $ rac{1}{______}$.
To simplify $64^{-1/2}$, the result is $ rac{1}{______}$.
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Match the expression with its simplified form:
Match the expression with its simplified form:
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Study Notes
GCSE Maths - Number: Powers, Roots and Fractional Indices
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Worksheet Focus: This worksheet provides practice questions on powers, roots, and fractional indices.
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Structure: Each section includes a worked example, a guided example, and further questions for independent practice.
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Section A: Focuses on calculating powers and roots.
- Worked Examples: Demonstrates finding powers (e.g., 133) and simplifying expressions with negative exponents (e.g., ()-4/54).
- Guided Examples: Similar types of problems.
- Student Practice: Provides basic questions on powers and root calculations. Examples include 73, 44, 56, (2/3)3, (4/5)4, 2-2
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Section B: Focuses on simplifying expressions with multiple powers.
- Worked Examples: Show how to simplify expressions like g5 × g3, (q6)11, y9÷ y2.
- Guided Examples: Similar simplification problems.
- Student Practice: Includes exercises in simplifying expressions combining powers and division with variable bases like x4x, a3 x a4, r10÷ r1, e4 x e7.
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Section C: Focuses on higher-level calculations involving simplifying surds, such as square roots
- Worked Examples: Explain how to simplify a square root by identifying square factors (e.g., √68 =2√17, √625 = 5).
- Guided Examples: Include similar types with practice problems
- Student Practice: Problems such as √81, √24, √900, √612, and others.
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Section D: Focuses on simplifying expressions with fractional or negative indices
- Worked Examples: Show step-by-step process for problems like 2-½
- Guided Examples: Similar types of problems
- Student Practice: Practice questions involve calculations like 9⅓, 12-½, and others.
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Section E: Focuses on estimating the value of square root problems
- Worked Examples: Demonstrate how to estimate square roots based on nearest perfect squares (e.g., estimating √14).
- Guided Examples: Provide examples with different numbers.
- Student Practice: Estimating √39, √35, √140, √18.2, √61, and similar problems.
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Description
This quiz is designed for GCSE students to practice calculating powers, roots, and fractional indices. It includes worked examples, guided examples, and a variety of practice questions. Review topics such as simplifying expressions and handling negative exponents to strengthen your understanding of mathematical concepts.
