Podcast
Questions and Answers
What is the estimated value of $6.5^{2}$?
What is the estimated value of $6.5^{2}$?
- 50
- 40 (correct)
- 36
- 45
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 (B)
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 ____.
Match the following expressions with their estimated values:
Match the following expressions with their estimated values:
What is the value of $7^3$?
What is the value of $7^3$?
The expression $5^{-2}$ equals to $ rac{1}{25}$.
The expression $5^{-2}$ equals to $ rac{1}{25}$.
What is the product of $4^4$ and $4^2$?
What is the product of $4^4$ and $4^2$?
The expression $2^{-3}$ can be rewritten as __________.
The expression $2^{-3}$ can be rewritten as __________.
Match the following powers with their results:
Match the following powers with their results:
The base can be negative when dealing with powers.
The base can be negative when dealing with powers.
What is the simplified form of $11^{-4}$?
What is the simplified form of $11^{-4}$?
$9^{-2} = rac{1}{81}$ is true.
$9^{-2} = rac{1}{81}$ is true.
What is the result of simplifying $( rac{1}{5^5})^{-1}$?
What is the result of simplifying $( rac{1}{5^5})^{-1}$?
The expression $2^{3} imes 2^{-2}$ simplifies to $2^{______}$.
The expression $2^{3} imes 2^{-2}$ simplifies to $2^{______}$.
Which of the following expressions represents a perfect square?
Which of the following expressions represents a perfect square?
Explain how to simplify $3^0$.
Explain how to simplify $3^0$.
To simplify $64^{-1/2}$, the result is $ rac{1}{______}$.
To simplify $64^{-1/2}$, the result is $ rac{1}{______}$.
Match the expression with its simplified form:
Match the expression with its simplified form:
Flashcards
Estimating square root of 14
Estimating square root of 14
Determining an approximate value for the square root of 14.
Estimating square root of a number
Estimating square root of a number
Finding an approximate value of a square root by positioning the number between two perfect squares.
Estimating 6.5²
Estimating 6.5²
Finding an approximate value for the square of 6.5.
Estimating square root of 39
Estimating square root of 39
Signup and view all the flashcards
Estimating square root of 140
Estimating square root of 140
Signup and view all the flashcards
Calculate 7³
Calculate 7³
Signup and view all the flashcards
Calculate 4⁴
Calculate 4⁴
Signup and view all the flashcards
Calculate 2⁻³
Calculate 2⁻³
Signup and view all the flashcards
Calculate 5⁻⁴ / 4
Calculate 5⁻⁴ / 4
Signup and view all the flashcards
Fractional Exponent
Fractional Exponent
Signup and view all the flashcards
Negative Exponent
Negative Exponent
Signup and view all the flashcards
Calculate 0.5⁵
Calculate 0.5⁵
Signup and view all the flashcards
Calculate 3²/⁵
Calculate 3²/⁵
Signup and view all the flashcards
Simplify 9^2
Simplify 9^2
Signup and view all the flashcards
Simplify 12^-2
Simplify 12^-2
Signup and view all the flashcards
Simplify 4^2/3
Simplify 4^2/3
Signup and view all the flashcards
Simplify 27^-3
Simplify 27^-3
Signup and view all the flashcards
Simplify 64^-12
Simplify 64^-12
Signup and view all the flashcards
Simplify 9^-12
Simplify 9^-12
Signup and view all the flashcards
Simplify 7^−3/8
Simplify 7^−3/8
Signup and view all the flashcards
Simplify 16^-4/81
Simplify 16^-4/81
Signup and view all the flashcards
Study Notes
GCSE Maths - Number: Powers, Roots and Fractional Indices
-
Worksheet Focus: This worksheet provides practice questions on powers, roots, and fractional indices.
-
Structure: Each section includes a worked example, a guided example, and further questions for independent practice.
-
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
-
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.
-
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.
-
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.
-
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
