Simplify: 3 1 / 4 + 1 1 / 5 − 2 13 / 20 3^{1/4} + 1^{1/5} - 2^{13/20} 3 1/4 + 1 1/5 − 2 13/20

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Introduction

In this article, we will simplify the given mathematical expression: $3^{1/4} + 1^{1/5} - 2^{13/20}$. This expression involves exponents and fractions, and we will use various mathematical techniques to simplify it.

Understanding Exponents and Fractions

Before we start simplifying the expression, let's review the basics of exponents and fractions.

• Exponents: An exponent is a small number that is written above and to the right of a number. It tells us how many times to multiply the number by itself. For example, $2^3$ means $2 \times 2 \times 2 = 8$.
• Fractions: A fraction is a way of expressing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, $\frac{1}{2}$ means one half.

Simplifying the Expression

Now that we have reviewed the basics of exponents and fractions, let's simplify the given expression.

Step 1: Simplify $3^{1/4}$

To simplify $3^{1/4}$, we need to find the fourth root of 3.

import math
result = math.pow(3, 1/4)
print(result)

The fourth root of 3 is approximately 1.316.

Step 2: Simplify $1^{1/5}$

To simplify $1^{1/5}$, we need to find the fifth root of 1.

import math
result = math.pow(1, 1/5)
print(result)

The fifth root of 1 is 1.

Step 3: Simplify $2^{13/20}$

To simplify $2^{13/20}$, we need to find the 13/20 power of 2.

import math
result = math.pow(2, 13/20)
print(result)

The 13/20 power of 2 is approximately 1.619.

Step 4: Combine the Simplified Expressions

Now that we have simplified each term, let's combine them.

import math
result = math.pow(3, 1/4) + math.pow(1, 1/5) - math.pow(2, 13/20)
print(result)

The final result is approximately 1.316 + 1 - 1.619 = 0.697.

Conclusion

In this article, we simplified the given mathematical expression: $3^{1/4} + 1^{1/5} - 2^{13/20}$. We used various mathematical techniques, including exponents and fractions, to simplify the expression. The final result is approximately 0.697.

Additional Resources

If you want to learn more about exponents and fractions, here are some additional resources:

• Khan Academy: Exponents and Fractions
• Mathway: Exponents and Fractions
• Wolfram Alpha: Exponents and Fractions

Frequently Asked Questions

Here are some frequently asked questions about simplifying the given expression:

• Q: What is the fourth root of 3? A: The fourth root of 3 is approximately 1.316.
• Q: What is the fifth root of 1? A: The fifth root of 1 is 1.
• Q: What is the 13/20 power of 2? A: The 13/20 power of 2 is approximately 1.619.

Related Articles

If you want to learn more about simplifying mathematical expressions, here are some related articles:

• Simplify: $2^3 + 4^2 - 1^5$
• Simplify: $5^2 + 3^4 - 2^6$
• Simplify: $7^3 + 2^5 - 3^2$
  Simplify: $3^{1/4} + 1^{1/5} - 2^{13/20}$ Q&A =====================================================

Introduction

In our previous article, we simplified the given mathematical expression: $3^{1/4} + 1^{1/5} - 2^{13/20}$. We used various mathematical techniques, including exponents and fractions, to simplify the expression. In this article, we will answer some frequently asked questions about simplifying the given expression.

Q&A

Q: What is the fourth root of 3?

A: The fourth root of 3 is approximately 1.316. This can be calculated using the formula: $3^{1/4} = \sqrt[4]{3}$.

Q: What is the fifth root of 1?

A: The fifth root of 1 is 1. This can be calculated using the formula: $1^{1/5} = \sqrt[5]{1}$.

Q: What is the 13/20 power of 2?

A: The 13/20 power of 2 is approximately 1.619. This can be calculated using the formula: $2^{13/20} = \sqrt[20]{2^{13}}$.

Q: How do I simplify the expression $3^{1/4} + 1^{1/5} - 2^{13/20}$?

A: To simplify the expression, you can use the following steps:

1. Simplify each term separately using the formulas above.
2. Combine the simplified terms using the formula: $a + b - c = (a + b) - c$.

Q: What is the final result of the expression $3^{1/4} + 1^{1/5} - 2^{13/20}$?

A: The final result of the expression is approximately 0.697.

Q: Can I use a calculator to simplify the expression?

A: Yes, you can use a calculator to simplify the expression. However, it's always a good idea to understand the mathematical concepts behind the calculation.

Q: How do I calculate the fourth root of 3 using a calculator?

A: To calculate the fourth root of 3 using a calculator, you can use the formula: $3^{1/4} = \sqrt[4]{3}$. Most calculators have a built-in function for calculating roots.

Q: How do I calculate the fifth root of 1 using a calculator?

A: To calculate the fifth root of 1 using a calculator, you can use the formula: $1^{1/5} = \sqrt[5]{1}$. Most calculators have a built-in function for calculating roots.

Q: How do I calculate the 13/20 power of 2 using a calculator?

A: To calculate the 13/20 power of 2 using a calculator, you can use the formula: $2^{13/20} = \sqrt[20]{2^{13}}$. Most calculators have a built-in function for calculating roots.

Conclusion

In this article, we answered some frequently asked questions about simplifying the given mathematical expression: $3^{1/4} + 1^{1/5} - 2^{13/20}$. We provided step-by-step instructions for simplifying the expression and answered questions about calculating roots using a calculator.

Additional Resources

If you want to learn more about simplifying mathematical expressions, here are some additional resources:

• Khan Academy: Exponents and Fractions
• Mathway: Exponents and Fractions
• Wolfram Alpha: Exponents and Fractions

Frequently Asked Questions

Here are some frequently asked questions about simplifying the given expression:

• Q: What is the fourth root of 3? A: The fourth root of 3 is approximately 1.316.
• Q: What is the fifth root of 1? A: The fifth root of 1 is 1.
• Q: What is the 13/20 power of 2? A: The 13/20 power of 2 is approximately 1.619.

Related Articles

If you want to learn more about simplifying mathematical expressions, here are some related articles:

• Simplify: $2^3 + 4^2 - 1^5$
• Simplify: $5^2 + 3^4 - 2^6$
• Simplify: $7^3 + 2^5 - 3^2$