Rewrite The Expression Without An Exponent Or Radical. 8 1 3 8^{\frac{1}{3}} 8 3 1 ​ Show Your Work Here:Hint: To Add The Nth Root Symbol ( □ □ (\sqrt[\square]{\square} ( □ □ ​ ], Type root.

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Understanding the Problem

The given expression is 8138^{\frac{1}{3}}. This expression involves an exponent, which is 13\frac{1}{3}. Our goal is to rewrite this expression without using an exponent or radical.

Rewriting the Expression

To rewrite the expression without an exponent or radical, we can use the definition of exponents. The expression 8138^{\frac{1}{3}} can be rewritten as the cube root of 8.

Using the nth Root Symbol

The nth root symbol is denoted by □□\sqrt[\square]{\square}. To type this symbol, we can use the "root" command. For example, to type the cube root symbol, we can use the command "root(3)".

Rewriting the Expression using the nth Root Symbol

Using the nth root symbol, we can rewrite the expression 8138^{\frac{1}{3}} as 83\sqrt[3]{8}.

Simplifying the Expression

The expression 83\sqrt[3]{8} can be simplified by finding the cube root of 8. The cube root of 8 is a number that, when multiplied by itself three times, gives 8.

Finding the Cube Root of 8

To find the cube root of 8, we can use the fact that 23=82^3 = 8. Therefore, the cube root of 8 is 2.

Rewriting the Expression without an Exponent or Radical

Using the fact that the cube root of 8 is 2, we can rewrite the expression 8138^{\frac{1}{3}} as 2.

Conclusion

In this article, we rewrote the expression 8138^{\frac{1}{3}} without using an exponent or radical. We used the definition of exponents and the nth root symbol to rewrite the expression as 83\sqrt[3]{8}. We then simplified the expression by finding the cube root of 8, which is 2.

Final Answer

The final answer is 2\boxed{2}.

Step-by-Step Solution

Step 1: Rewrite the expression using the nth root symbol

The expression 8138^{\frac{1}{3}} can be rewritten as 83\sqrt[3]{8}.

Step 2: Simplify the expression

The expression 83\sqrt[3]{8} can be simplified by finding the cube root of 8.

Step 3: Find the cube root of 8

The cube root of 8 is a number that, when multiplied by itself three times, gives 8. We can use the fact that 23=82^3 = 8 to find the cube root of 8.

Step 4: Rewrite the expression without an exponent or radical

Using the fact that the cube root of 8 is 2, we can rewrite the expression 8138^{\frac{1}{3}} as 2.

Mathematical Proof

Theorem

The cube root of 8 is 2.

Proof

We can prove this theorem by showing that 23=82^3 = 8. This is true, since 23=82^3 = 8. Therefore, the cube root of 8 is 2.

Corollary

The expression 8138^{\frac{1}{3}} can be rewritten as 2.

Proof

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to rewriting the expression 8138^{\frac{1}{3}} without using an exponent or radical.

Q: What is the definition of an exponent?

A: An exponent is a small number that is written above and to the right of a number or a variable. It represents the power to which the base is raised.

Q: How do I rewrite the expression 8138^{\frac{1}{3}} without using an exponent or radical?

A: To rewrite the expression 8138^{\frac{1}{3}} without using an exponent or radical, we can use the definition of exponents. The expression 8138^{\frac{1}{3}} can be rewritten as the cube root of 8.

Q: What is the cube root of 8?

A: The cube root of 8 is a number that, when multiplied by itself three times, gives 8. We can use the fact that 23=82^3 = 8 to find the cube root of 8.

Q: How do I find the cube root of 8?

A: To find the cube root of 8, we can use the fact that 23=82^3 = 8. This means that the cube root of 8 is 2.

Q: Can I use the nth root symbol to rewrite the expression 8138^{\frac{1}{3}}?

A: Yes, you can use the nth root symbol to rewrite the expression 8138^{\frac{1}{3}}. The nth root symbol is denoted by □□\sqrt[\square]{\square}. To type this symbol, you can use the "root" command.

Q: How do I type the nth root symbol?

A: To type the nth root symbol, you can use the "root" command. For example, to type the cube root symbol, you can use the command "root(3)".

Q: What is the final answer to the expression 8138^{\frac{1}{3}}?

A: The final answer to the expression 8138^{\frac{1}{3}} is 2.

Common Mistakes

Mistake 1: Not using the definition of exponents

Not using the definition of exponents can lead to incorrect rewriting of the expression.

Mistake 2: Not finding the cube root of 8

Not finding the cube root of 8 can lead to incorrect rewriting of the expression.

Mistake 3: Not using the nth root symbol

Not using the nth root symbol can lead to incorrect rewriting of the expression.

Tips and Tricks

Tip 1: Use the definition of exponents

Using the definition of exponents can help you rewrite the expression correctly.

Tip 2: Find the cube root of 8

Finding the cube root of 8 can help you rewrite the expression correctly.

Tip 3: Use the nth root symbol

Using the nth root symbol can help you rewrite the expression correctly.

Conclusion

In this article, we answered some frequently asked questions related to rewriting the expression 8138^{\frac{1}{3}} without using an exponent or radical. We also provided some tips and tricks to help you rewrite the expression correctly.

Final Answer

The final answer is 2\boxed{2}.