10 Questions
Explain the meaning of exponentiation and provide an example of an exponentiation operation.
Exponentiation is an operation involving two numbers, the base and the exponent or power. It is written as $b^n$, where $b$ is the base and $n$ is the power. An example of exponentiation is $2^3$, where 2 is the base and 3 is the power.
What does $b^n$ represent when $n$ is a positive integer?
When $n$ is a positive integer, $b^n$ represents the product of multiplying $n$ bases, which corresponds to repeated multiplication of the base.
How is the exponent usually shown in exponentiation?
The exponent is usually shown as a superscript to the right of the base.
Provide at least three different ways to refer to $b^n$.
Three different ways to refer to $b^n$ are 'b raised to the nth power', 'b to the nth power', and 'the nth power of b'.
What does the statement 'for any positive integer $n$, $b^n$ is $n$ occurrences of $b$ all multiplied by each other' imply about exponentiation?
It implies that when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents can be added together to obtain the product of the bases.
In the context of exponentiation, what does the statement 'for any positive integer $n$, $b^n$ is $n$ occurrences of $b$ all multiplied by each other' imply about the relationship between the base and the exponent?
The statement implies that when the base $b$ is raised to the power of a positive integer $n$, it results in the product of multiplying $n$ occurrences of $b$ together, illustrating the relationship between the base and the exponent in exponentiation.
What property of exponentiation directly follows from the fact that for any positive integer $n$, $b^n$ is the product of multiplying $n$ bases together?
The property that directly follows is that exponentiation corresponds to repeated multiplication of the base when the exponent is a positive integer.
Explain at least three different ways to refer to the expression $b^n$ in the context of exponentiation.
Three different ways to refer to the expression $b^n$ are 'b raised to the nth power', 'b to the power of n', and 'the nth power of b'.
Provide an example of an exponentiation operation, demonstrating the meaning of exponentiation.
An example of an exponentiation operation is $2^3$, which represents '2 raised to the power of 3' and equals 8. This demonstrates that exponentiation involves repeated multiplication of the base.
How is the exponent usually shown in the context of exponentiation?
The exponent is usually shown as a superscript to the right of the base in the context of exponentiation.
Study Notes
Exponentiation
- Exponentiation is a mathematical operation involving two numbers: the base and the exponent or power.
- It is written as bn, where b is the base and n is the power, pronounced as "b (raised) to the power of n".
- When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: bn is the product of multiplying n bases.
- The exponent is usually shown as a superscript to the right of the base.
- bn can be called "b raised to the nth power", "b (raised) to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth".
Properties of Exponentiation
- For any positive integer n, bn is n occurrences of b all multiplied by each other.
- When multiplying a base raised to one exponent by the same base raised to another exponent, several properties of exponentiation directly follow.
Test your knowledge of exponentiation with this quiz! Explore the principles of raising a base to a power and grasp the concept of repeated multiplication. Sharpen your understanding of exponents and power operations through a series of engaging questions.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
