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Questions and Answers
Which of the following expressions are equal?
Which of the following expressions are equal?
A³b² and a²b³ are the same expression.
A³b² and a²b³ are the same expression.
False
What is the value of 2⁸?
What is the value of 2⁸?
256
The expression a²b³ can also be written as __________.
The expression a²b³ can also be written as __________.
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Match each expression with its equivalent:
Match each expression with its equivalent:
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Which of the following numbers is equivalent to $10^5$?
Which of the following numbers is equivalent to $10^5$?
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The number $10^3$ is read as ten raised to the power of three.
The number $10^3$ is read as ten raised to the power of three.
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What is the base in the expression $81 = 3^4$?
What is the base in the expression $81 = 3^4$?
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The mass of Uranus is approximately _____ kg.
The mass of Uranus is approximately _____ kg.
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Match the following numbers with their exponential forms:
Match the following numbers with their exponential forms:
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What is the value of $10^2$?
What is the value of $10^2$?
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Exponents can only have a base of 10.
Exponents can only have a base of 10.
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What is the exponential form of 1,000?
What is the exponential form of 1,000?
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What is the simplified form of $(2^3)^2$?
What is the simplified form of $(2^3)^2$?
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$(52)^3$ is greater than $(52) imes 3$.
$(52)^3$ is greater than $(52) imes 3$.
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What is the result of $(7^2)^{10}$?
What is the result of $(7^2)^{10}$?
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The expression $(a^m)^n$ can be simplified to $a^{______}$.
The expression $(a^m)^n$ can be simplified to $a^{______}$.
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Match the following expressions with their simplified forms:
Match the following expressions with their simplified forms:
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What is the result of simplifying $2^3 imes 3^3$?
What is the result of simplifying $2^3 imes 3^3$?
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The result of $(2^2)^{100}$ is equal to $2^{200}$.
The result of $(2^2)^{100}$ is equal to $2^{200}$.
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If $a$ is a non-zero integer and $m$ and $n$ are whole numbers, what is the general formula for $(a^m)^n$?
If $a$ is a non-zero integer and $m$ and $n$ are whole numbers, what is the general formula for $(a^m)^n$?
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The expression $3^5$ equals $3 imes 3 imes 3 imes 3 imes 3$.
The expression $3^5$ equals $3 imes 3 imes 3 imes 3 imes 3$.
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According to the laws of exponents, $a^m imes a^n$ equals __________.
According to the laws of exponents, $a^m imes a^n$ equals __________.
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Match the following exponent values with their results:
Match the following exponent values with their results:
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What is the result of $35 imes 0$?
What is the result of $35 imes 0$?
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Calculate the value of $2^4$.
Calculate the value of $2^4$.
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The expression $23 > 52$ is true.
The expression $23 > 52$ is true.
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What is the result of simplifying $32 × 34 × 38$?
What is the result of simplifying $32 × 34 × 38$?
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The expression $7^0$ is equal to 7.
The expression $7^0$ is equal to 7.
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Simplify $615 ÷ 610$ and express in exponential form.
Simplify $615 ÷ 610$ and express in exponential form.
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The result of $a^3 × a^2$ is $a^{______}$.
The result of $a^3 × a^2$ is $a^{______}$.
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What is the simplified form of $(2^3 × 4) ÷ 3 × 32$?
What is the simplified form of $(2^3 × 4) ÷ 3 × 32$?
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The expression $10 × 10^{11} = 100^{11}$.
The expression $10 × 10^{11} = 100^{11}$.
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Match the following expressions with their exponential results:
Match the following expressions with their exponential results:
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What is the simplified form of the expression $8t ÷ 82$?
What is the simplified form of the expression $8t ÷ 82$?
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Express the number 120719 in standard form.
Express the number 120719 in standard form.
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The distance from the Sun to Earth is less than 1.5 × 10^11 m.
The distance from the Sun to Earth is less than 1.5 × 10^11 m.
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What is the standard form of the number 3,430,000?
What is the standard form of the number 3,430,000?
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The standard form of the number 70,040,000,000 is __________.
The standard form of the number 70,040,000,000 is __________.
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Match the following distances with their standard forms:
Match the following distances with their standard forms:
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Which of the following numbers is written in expanded form as 4 × 10^5 + 5 × 10^3 + 3 × 10^2 + 2 × 10^0?
Which of the following numbers is written in expanded form as 4 × 10^5 + 5 × 10^3 + 3 × 10^2 + 2 × 10^0?
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In the number 5.9853 × 10^3, the exponent indicates that the decimal point is moved three places to the right.
In the number 5.9853 × 10^3, the exponent indicates that the decimal point is moved three places to the right.
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Convert the number 30,000,000,000,000 to standard form.
Convert the number 30,000,000,000,000 to standard form.
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Study Notes
Exponents and Powers
- Exponents provide a shorter way to write large numbers
- Large numbers are difficult to read and compare
- Exponents are used to represent repeated multiplication
- The number being multiplied is called the base
- The number of times the base is multiplied is called the exponent
- For example, 10,000 = 10 × 10 × 10 × 10 = 10⁴ (10 to the fourth power)
Exponential Notation
- Large numbers can be written concisely using exponents
- The base is repeatedly multiplied
- The exponent indicates the number of times the base is used in multiplication
- For example, 1,000 = 10 x 10 x 10 = 103 (base 10, exponent 3)
Laws of Exponents
- Multiplying powers with the same base: Add the exponents
- For example, 2² x 2³ = 2^(2+3) = 2⁵
- Dividing powers with the same base: Subtract the exponents
- For example, 2⁵ / 2² = 2^(5-2) = 2³
- Power of a power: Multiply the exponents
- For example, (2²)³ = 2^(2x3) = 2⁶
- Multiplying powers with the same exponent: Multiply the bases
- For example, 2³ x 3³ = (2x3)³ = 6³
- Dividing powers with the same exponent: Divide the bases
- For example, 6³ / 2³ = (6/2)³ = 3³
- Zero exponent: Any non-zero number to the power of zero is equal to 1
- a⁰ = 1 (e.g., 5⁰ = 1, 10⁰ = 1)
Standard Form of Large Numbers
- Write numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer
- Used to represent extremely large or small numbers concisely
- For example, 300,000,000 = 3 × 10⁸
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Description
Test your understanding of algebraic expressions and exponents with this quiz. Determine equivalence, simplify expressions, and convert between standard and exponential forms. This quiz is perfect for students studying algebra concepts and looking to strengthen their skills.
