What Is $6^4$ Written In Expanded Form?A. $4+4+4+4+4+4$ B. $4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$ C. $6+6+6+6$ D. $6 \cdot 6 \cdot 6 \cdot 6$

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Understanding Exponents and Expanded Form

In mathematics, exponents are a shorthand way of representing repeated multiplication. When we see an expression like $6^4$, we know that it means $6$ multiplied by itself $4$ times. In this article, we will explore what $6^4$ written in expanded form means and how to calculate it.

What is Expanded Form?

Expanded form is a way of writing a number or an expression by breaking it down into its individual components. For example, the expanded form of the number $12$ is $10 + 2$. Similarly, the expanded form of the expression $6^4$ is a way of writing it as a sum of repeated multiplications.

Calculating $6^4$

To calculate $6^4$, we need to multiply $6$ by itself $4$ times. This can be written as:

$$6^4 = 6 \cdot 6 \cdot 6 \cdot 6$$

Why is this the Correct Answer?

The correct answer is $6 \cdot 6 \cdot 6 \cdot 6$ because it represents the repeated multiplication of $6$ by itself $4$ times. This is the definition of an exponent, and it is the only way to accurately represent $6^4$ in expanded form.

Why are the Other Options Incorrect?

Let's take a closer look at the other options:

• Option A: $4+4+4+4+4+4$. This option is incorrect because it represents the sum of $6$ numbers, not the product of $6$ numbers.
• Option C: $6+6+6+6$. This option is incorrect because it represents the sum of $4$ numbers, not the product of $6$ numbers.
• Option D: $6 \cdot 6 \cdot 6 \cdot 6$. This option is incorrect because it represents the product of $4$ numbers, not $6$ numbers.

Conclusion

In conclusion, $6^4$ written in expanded form is $6 \cdot 6 \cdot 6 \cdot 6$. This represents the repeated multiplication of $6$ by itself $4$ times, which is the definition of an exponent. The other options are incorrect because they do not accurately represent the product of $6$ numbers.

Frequently Asked Questions

Q: What is the definition of an exponent?

A: An exponent is a shorthand way of representing repeated multiplication. For example, $6^4$ means $6$ multiplied by itself $4$ times.

Q: How do I calculate $6^4$?

A: To calculate $6^4$, you need to multiply $6$ by itself $4$ times. This can be written as $6 \cdot 6 \cdot 6 \cdot 6$.

Q: Why is $6 \cdot 6 \cdot 6 \cdot 6$ the correct answer?

A: $6 \cdot 6 \cdot 6 \cdot 6$ is the correct answer because it represents the repeated multiplication of $6$ by itself $4$ times, which is the definition of an exponent.

Q: Why are the other options incorrect?

A: The other options are incorrect because they do not accurately represent the product of $6$ numbers. Option A represents the sum of $6$ numbers, Option C represents the sum of $4$ numbers, and Option D represents the product of $4$ numbers.

Additional Resources

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

• Khan Academy: Exponents and Powers
• Mathway: Exponents and Expanded Form
• Wolfram MathWorld: Exponents and Expanded Form

Final Thoughts

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Frequently Asked Questions

Q: What is the definition of an exponent?

A: An exponent is a shorthand way of representing repeated multiplication. For example, $6^4$ means $6$ multiplied by itself $4$ times.

Q: How do I calculate $6^4$?

A: To calculate $6^4$, you need to multiply $6$ by itself $4$ times. This can be written as $6 \cdot 6 \cdot 6 \cdot 6$.

Q: Why is $6 \cdot 6 \cdot 6 \cdot 6$ the correct answer?

A: $6 \cdot 6 \cdot 6 \cdot 6$ is the correct answer because it represents the repeated multiplication of $6$ by itself $4$ times, which is the definition of an exponent.

Q: Why are the other options incorrect?

A: The other options are incorrect because they do not accurately represent the product of $6$ numbers. Option A represents the sum of $6$ numbers, Option C represents the sum of $4$ numbers, and Option D represents the product of $4$ numbers.

Q: What is the difference between an exponent and a power?

A: An exponent is a shorthand way of representing repeated multiplication, while a power is a number raised to a certain power. For example, $6^4$ is an exponent, while $6$ to the power of $4$ is a power.

Q: How do I simplify an expression with an exponent?

A: To simplify an expression with an exponent, you need to multiply the base number by itself as many times as the exponent indicates. For example, $6^4$ can be simplified as $6 \cdot 6 \cdot 6 \cdot 6$.

Q: What is the order of operations for exponents?

A: The order of operations for exponents is to evaluate the expression inside the exponent first, and then multiply the base number by itself as many times as the exponent indicates. For example, $6^{4+2}$ can be simplified as $6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6$.

Q: Can I use exponents with fractions?

A: Yes, you can use exponents with fractions. For example, $1/2^3$ can be simplified as $1/8$.

Q: Can I use exponents with decimals?

A: Yes, you can use exponents with decimals. For example, $2.5^3$ can be simplified as $15.625$.

Q: What is the rule for multiplying exponents with the same base?

A: When multiplying exponents with the same base, you add the exponents. For example, $2^3 \cdot 2^4$ can be simplified as $2^{3+4} = 2^7$.

Q: What is the rule for dividing exponents with the same base?

A: When dividing exponents with the same base, you subtract the exponents. For example, $2^5 / 2^3$ can be simplified as $2^{5-3} = 2^2$.

Q: Can I use exponents with negative numbers?

A: Yes, you can use exponents with negative numbers. For example, $(-2)^3$ can be simplified as $-8$.

Q: Can I use exponents with zero?

A: Yes, you can use exponents with zero. For example, $0^3$ can be simplified as $0$.

Q: Can I use exponents with one?

A: Yes, you can use exponents with one. For example, $1^3$ can be simplified as $1$.

Additional Resources

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

• Khan Academy: Exponents and Powers
• Mathway: Exponents and Expanded Form
• Wolfram MathWorld: Exponents and Expanded Form

Final Thoughts

In conclusion, exponents and expanded form are important concepts in mathematics that can be used to simplify complex expressions. We hope this article has helped you understand exponents and expanded form better. If you have any questions or need further clarification, please don't hesitate to ask.