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Questions and Answers
What is the value of $4^3$?
What is the value of $4^3$?
Which expression represents 'a raised to the power of 5'?
Which expression represents 'a raised to the power of 5'?
In the expression $7^4$, which number is the base?
In the expression $7^4$, which number is the base?
What does the expression $(-3)^2$ equal?
What does the expression $(-3)^2$ equal?
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Which of the following is equivalent to $3^2 \times 2^3$?
Which of the following is equivalent to $3^2 \times 2^3$?
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Which of these is the correct exponential representation of 64 as a power of 4?
Which of these is the correct exponential representation of 64 as a power of 4?
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How can the expression $a \times a \times b \times b \times b$ be written in exponential form?
How can the expression $a \times a \times b \times b \times b$ be written in exponential form?
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What is the value of $4^2$ + $2^3$?
What is the value of $4^2$ + $2^3$?
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Which of the following describes how the expression $5x^2 - 3$ is formed?
Which of the following describes how the expression $5x^2 - 3$ is formed?
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What is the correct way to describe how the expression $2ab + 5$ is formed?
What is the correct way to describe how the expression $2ab + 5$ is formed?
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How should we describe the formation of the expression $x^3$?
How should we describe the formation of the expression $x^3$?
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Which of these correctly explains how the expression $3x^2 - 5x$ is formed?
Which of these correctly explains how the expression $3x^2 - 5x$ is formed?
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What is the first operation performed to form the expression $10y - 20$?
What is the first operation performed to form the expression $10y - 20$?
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What operation is used to obtain the term $xy$?
What operation is used to obtain the term $xy$?
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How is the expression $4xy + 7$ formed?
How is the expression $4xy + 7$ formed?
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Which of the expressions is formed by first multiplying a variable by itself and then multiplying this result by 2?
Which of the expressions is formed by first multiplying a variable by itself and then multiplying this result by 2?
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Which of the following correctly represents the expansion of the term $a^4$?
Which of the following correctly represents the expansion of the term $a^4$?
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What is the numerical coefficient of the term $-12pqr$?
What is the numerical coefficient of the term $-12pqr$?
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In the term $7ab^2$, what is the coefficient of $b^2$?
In the term $7ab^2$, what is the coefficient of $b^2$?
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If a term has a coefficient of '$-1$', how is it typically written?
If a term has a coefficient of '$-1$', how is it typically written?
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What is the coefficient of $x$ in the term $x$?
What is the coefficient of $x$ in the term $x$?
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In the expression $9jkl$, what is the coefficient of $9l$?
In the expression $9jkl$, what is the coefficient of $9l$?
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Which of the following is the correct way to express the term $y \times y \times y$, using exponents?
Which of the following is the correct way to express the term $y \times y \times y$, using exponents?
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In the term $15p^2q$, what is the coefficient of $15q$?
In the term $15p^2q$, what is the coefficient of $15q$?
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In the expression $13 - y + 5y^2$, what is the numerical coefficient of the term $-y$?
In the expression $13 - y + 5y^2$, what is the numerical coefficient of the term $-y$?
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What is the numerical coefficient of the term $4p^2q$ in the expression $4p^2q - 3pq^2 + 5$?
What is the numerical coefficient of the term $4p^2q$ in the expression $4p^2q - 3pq^2 + 5$?
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In the expression $4x - 3y$, what is the coefficient of $x$?
In the expression $4x - 3y$, what is the coefficient of $x$?
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What is the coefficient of $y$ in the expression $8 + yz$?
What is the coefficient of $y$ in the expression $8 + yz$?
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In the expression $my + m$, what is the coefficient of $y$?
In the expression $my + m$, what is the coefficient of $y$?
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Which of the following terms are like terms?
Which of the following terms are like terms?
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Which of the following is an example of unlike terms?
Which of the following is an example of unlike terms?
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Which pair of terms are considered 'like terms'?
Which pair of terms are considered 'like terms'?
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What is the correct algebraic expression for 'One-half of the sum of numbers x and y'?
What is the correct algebraic expression for 'One-half of the sum of numbers x and y'?
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Which option represents 'Numbers x and y both squared and added'?
Which option represents 'Numbers x and y both squared and added'?
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Which of the following expressions represents 'Product of numbers y and z subtracted from 10'?
Which of the following expressions represents 'Product of numbers y and z subtracted from 10'?
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Which of these is NOT a factor of the term –4ab?
Which of these is NOT a factor of the term –4ab?
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Given the terms pq² and – 4pq², which statement is correct?
Given the terms pq² and – 4pq², which statement is correct?
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Which algebraic expression correctly represents 'Sum of numbers a and b subtracted from their product'?
Which algebraic expression correctly represents 'Sum of numbers a and b subtracted from their product'?
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Considering only the variables and their powers, which pair are NOT like terms?
Considering only the variables and their powers, which pair are NOT like terms?
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A circular garden has a diameter of 21 meters. What is the length of rope needed to fence the garden twice?
A circular garden has a diameter of 21 meters. What is the length of rope needed to fence the garden twice?
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What is the radius of a circle whose circumference is 154 meters?
What is the radius of a circle whose circumference is 154 meters?
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A circle has a radius of 14 mm. What is its approximate area?
A circle has a radius of 14 mm. What is its approximate area?
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If a circular sheet has a radius of 5 cm, what is its approximate area?
If a circular sheet has a radius of 5 cm, what is its approximate area?
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A gardener needs to fence a circular garden with a diameter of 21 m, and the rope costs $4 per meter. What will be the total cost of the rope for two rounds of fence?
A gardener needs to fence a circular garden with a diameter of 21 m, and the rope costs $4 per meter. What will be the total cost of the rope for two rounds of fence?
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A circular sheet with a radius of 4 cm has a circle of radius 3 cm removed from it. What is the area of the remaining sheet? (Use π = 3.14)
A circular sheet with a radius of 4 cm has a circle of radius 3 cm removed from it. What is the area of the remaining sheet? (Use π = 3.14)
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What is the area of a circle with a diameter of 49 meters?
What is the area of a circle with a diameter of 49 meters?
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A circle has a radius of 21 cm. What is its circumference?
A circle has a radius of 21 cm. What is its circumference?
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Study Notes
Exponents and Powers
- Large numbers can be written in a shorter form using exponents.
- 10,000 = 10 × 10 × 10 × 10 = 104
- '10' is the base, '4' is the exponent.
- 104 is read as 'ten raised to the power of four' or 'ten to the power four' or 'fourth power of 10'
- 1000 = 10 × 10 × 10 = 103
- 100,000 = 10 × 10 × 10 × 10 × 10 = 105
- In exponential form, the base is the number being multiplied and the exponent is how many times the base is multiplied.
Expanding Numbers
- 47561 = (4 × 10,000) + (7 × 1000) + (5 × 100) + (6 × 10) + 1
- 47561 = (4 × 104) + (7 × 103) + (5 × 102) + (6 × 101) + (1 × 100)
Laws of Exponents
- am × an = a(m + n)
- am ÷ an = a(m – n)
- (am)n = a(m × n)
- am × bm = (ab)m
- a0 = 1 (any non-zero integer a)
Taking Power of a Power
- (am)n = a(m × n)
- (23)2 = 2(3 × 2) = 26 = 64
Dividing Powers with the Same Base
- am ÷ an = a(m – n)
- 37 ÷ 34 = 3(7 – 4) = 33 = 27
Taking Power of a Power
- (am)n = a(m × n)
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Description
Test your understanding of exponents and how expressions are formed. This quiz covers various aspects of exponential notation and the structure of algebraic expressions. Challenge your knowledge with a variety of questions related to these topics.
