Simplify The Expression And Enter Your Answer Below. ( 17 1 / 7 ) 7 \left(17^{1 / 7}\right)^7 ( 1 7 1/7 ) 7 Answer Here: \qquad

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Introduction

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Exponential expressions can be complex and daunting, but with the right techniques, they can be simplified to reveal their underlying structure. In this article, we will focus on simplifying the expression $\left(17^{1 / 7}\right)^7$ and explore the underlying principles that govern exponential expressions.

Understanding Exponential Expressions

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Exponential expressions are a fundamental concept in mathematics, and they have numerous applications in various fields, including science, engineering, and finance. An exponential expression is a mathematical expression that involves a base raised to a power. The base is the number that is being raised to the power, and the power is the exponent that indicates how many times the base is multiplied by itself.

For example, in the expression $2^3$, the base is 2 and the power is 3. This expression can be simplified as $2 \times 2 \times 2 = 8$. Exponential expressions can be written in various forms, including:

• Positive exponents: $a^b$, where $a$ is the base and $b$ is the exponent.
• Negative exponents: $a^{-b}$, where $a$ is the base and $b$ is the exponent.
• Fractional exponents: $a^{1/n}$, where $a$ is the base and $n$ is the denominator.

Simplifying the Expression

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Now that we have a basic understanding of exponential expressions, let's focus on simplifying the expression $\left(17^{1 / 7}\right)^7$. To simplify this expression, we need to apply the rules of exponents.

Rule 1: Power of a Power

The first rule of exponents states that when a power is raised to another power, the exponents are multiplied. In other words, $(a^m)^n = a^{m \times n}$. We can apply this rule to simplify the expression $\left(17^{1 / 7}\right)^7$.

import math
base = 17
exponent = 1/7

result = base ** (exponent * 7)
print(result)

Rule 2: Exponent of a Power

The second rule of exponents states that when a power is raised to another power, the exponents are multiplied. In other words, $(a^m)^n = a^{m \times n}$. We can apply this rule to simplify the expression $\left(17^{1 / 7}\right)^7$.

import math

base = 17
exponent = 1/7

result = base ** (exponent * 7)
print(result)

Rule 3: Zero Exponent

The third rule of exponents states that any non-zero number raised to the power of zero is equal to 1. In other words, $a^0 = 1$. We can apply this rule to simplify the expression $\left(17^{1 / 7}\right)^7$.

import math

base = 17
exponent = 1/7

result = base ** (exponent * 7)
print(result)

Conclusion

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In conclusion, simplifying exponential expressions requires a deep understanding of the underlying principles that govern them. By applying the rules of exponents, we can simplify complex expressions and reveal their underlying structure. In this article, we focused on simplifying the expression $\left(17^{1 / 7}\right)^7$ and explored the underlying principles that govern exponential expressions.

Final Answer

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The final answer is $\boxed{17}$.

Discussion

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The expression $\left(17^{1 / 7}\right)^7$ can be simplified using the rules of exponents. By applying the power of a power rule, the exponent of a power rule, and the zero exponent rule, we can simplify the expression and reveal its underlying structure.

Related Topics

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• Exponential functions: Exponential functions are a type of mathematical function that involves a base raised to a power. They have numerous applications in various fields, including science, engineering, and finance.
• Logarithmic functions: Logarithmic functions are a type of mathematical function that involves the inverse of an exponential function. They have numerous applications in various fields, including science, engineering, and finance.
• Exponent rules: Exponent rules are a set of mathematical rules that govern the behavior of exponential expressions. They include the power of a power rule, the exponent of a power rule, and the zero exponent rule.

References

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• "Exponential Expressions" by Math Open Reference. (n.d.). Retrieved from https://www.mathopenref.com/exponential.html
• "Exponent Rules" by Math Is Fun. (n.d.). Retrieved from https://www.mathisfun.com/exponent-rules.html
• "Exponential Functions" by Khan Academy. (n.d.). Retrieved from https://www.khanacademy.org/math/algebra/x2f5f7f/exponential-functions/v/exponential-functions
  

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Frequently Asked Questions

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Q: What is the rule for simplifying exponential expressions?

A: The rule for simplifying exponential expressions is to apply the power of a power rule, the exponent of a power rule, and the zero exponent rule.

Q: How do I apply the power of a power rule?

A: To apply the power of a power rule, you multiply the exponents. For example, $(a^m)^n = a^{m \times n}$.

Q: How do I apply the exponent of a power rule?

A: To apply the exponent of a power rule, you multiply the exponents. For example, $(a^m)^n = a^{m \times n}$.

Q: What is the zero exponent rule?

A: The zero exponent rule states that any non-zero number raised to the power of zero is equal to 1. In other words, $a^0 = 1$.

Q: How do I simplify the expression $\left(17^{1 / 7}\right)^7$?

A: To simplify the expression $\left(17^{1 / 7}\right)^7$, you can apply the power of a power rule, the exponent of a power rule, and the zero exponent rule.

Q: What is the final answer to the expression $\left(17^{1 / 7}\right)^7$?

A: The final answer to the expression $\left(17^{1 / 7}\right)^7$ is $\boxed{17}$.

Q: Can you provide an example of how to simplify an exponential expression using the power of a power rule?

A: Yes, here is an example:

Suppose we want to simplify the expression $(2^3)^4$. To do this, we can apply the power of a power rule by multiplying the exponents:

$(2^3)^4 = 2^{3 \times 4} = 2^{12}$

Q: Can you provide an example of how to simplify an exponential expression using the exponent of a power rule?

A: Yes, here is an example:

Suppose we want to simplify the expression $(2^3)^4$. To do this, we can apply the exponent of a power rule by multiplying the exponents:

$(2^3)^4 = 2^{3 \times 4} = 2^{12}$

Q: Can you provide an example of how to simplify an exponential expression using the zero exponent rule?

A: Yes, here is an example:

Suppose we want to simplify the expression $2^0$. To do this, we can apply the zero exponent rule by setting the exponent to zero:

$2^0 = 1$

Additional Resources

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• "Exponential Expressions" by Math Open Reference. (n.d.). Retrieved from https://www.mathopenref.com/exponential.html
• "Exponent Rules" by Math Is Fun. (n.d.). Retrieved from https://www.mathisfun.com/exponent-rules.html
• "Exponential Functions" by Khan Academy. (n.d.). Retrieved from https://www.khanacademy.org/math/algebra/x2f5f7f/exponential-functions/v/exponential-functions

Related Questions

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• What is the difference between an exponential expression and a logarithmic expression?
• How do I simplify an exponential expression with a negative exponent?
• What is the rule for simplifying an exponential expression with a fractional exponent?