Evaluate $4^3$.

Introduction

Understanding Exponents Exponents are a fundamental concept in mathematics, used to represent repeated multiplication of a number. In this article, we will focus on evaluating the expression $4^3$, which involves raising 4 to the power of 3. This expression can be evaluated using the rules of exponents, and we will explore the different methods to simplify it.

Evaluating $4^3$ using the Definition of Exponents

The expression $4^3$ can be evaluated using the definition of exponents, which states that $a^b$ represents the product of $a$ multiplied by itself $b$ times. In this case, $4^3$ represents the product of 4 multiplied by itself 3 times.

$$4^3 = 4 \times 4 \times 4$$

To evaluate this expression, we can multiply 4 by itself 3 times, which gives us:

$$4^3 = 4 \times 4 \times 4 = 64$$

Evaluating $4^3$ using the Rule of Exponents

Another way to evaluate $4^3$ is by using the rule of exponents, which states that $a^b \times a^c = a^{b+c}$. In this case, we can rewrite $4^3$ as:

$$4^3 = 4 \times 4 \times 4 = 4^1 \times 4^1 \times 4^1$$

Using the rule of exponents, we can simplify this expression as:

$$4^3 = 4^1 \times 4^1 \times 4^1 = 4^{1+1+1} = 4^3$$

Evaluating $4^3$ using the Property of Exponents

The property of exponents states that $a^m \times a^n = a^{m+n}$. In this case, we can rewrite $4^3$ as:

$$4^3 = 4 \times 4 \times 4 = 4^1 \times 4^1 \times 4^1$$

Using the property of exponents, we can simplify this expression as:

$$4^3 = 4^1 \times 4^1 \times 4^1 = 4^{1+1+1} = 4^3$$

Evaluating $4^3$ using the Formula for Exponents

The formula for exponents states that $a^b = a \times a \times ... \times a$ (b times). In this case, we can rewrite $4^3$ as:

$$4^3 = 4 \times 4 \times 4$$

Using the formula for exponents, we can simplify this expression as:

$$4^3 = 4 \times 4 \times 4 = 64$$

Conclusion

In this article, we have evaluated the expression $4^3$ using different methods, including the definition of exponents, the rule of exponents, the property of exponents, and the formula for exponents. Each of these methods has given us the same result, which is $4^3 = 64$. This demonstrates the power and flexibility of exponents in mathematics.

Frequently Asked Questions

• What is the definition of exponents? The definition of exponents states that $a^b$ represents the product of $a$ multiplied by itself $b$ times.
• How do you evaluate $4^3$ using the definition of exponents? To evaluate $4^3$ using the definition of exponents, you can multiply 4 by itself 3 times, which gives us $4^3 = 4 \times 4 \times 4 = 64$.
• What is the rule of exponents? The rule of exponents states that $a^b \times a^c = a^{b+c}$.
• How do you evaluate $4^3$ using the rule of exponents? To evaluate $4^3$ using the rule of exponents, you can rewrite $4^3$ as $4^1 \times 4^1 \times 4^1$ and simplify it as $4^{1+1+1} = 4^3$.
• What is the property of exponents? The property of exponents states that $a^m \times a^n = a^{m+n}$.
• How do you evaluate $4^3$ using the property of exponents? To evaluate $4^3$ using the property of exponents, you can rewrite $4^3$ as $4^1 \times 4^1 \times 4^1$ and simplify it as $4^{1+1+1} = 4^3$.
• What is the formula for exponents? The formula for exponents states that $a^b = a \times a \times ... \times a$ (b times).
• How do you evaluate $4^3$ using the formula for exponents? To evaluate $4^3$ using the formula for exponents, you can rewrite $4^3$ as $4 \times 4 \times 4$ and simplify it as $64$.

Further Reading

• Exponents and Powers Exponents and powers are a fundamental concept in mathematics, used to represent repeated multiplication of a number. In this article, we have evaluated the expression $4^3$ using different methods, including the definition of exponents, the rule of exponents, the property of exponents, and the formula for exponents.
• Mathematical Operations Mathematical operations, such as addition, subtraction, multiplication, and division, are used to perform calculations and solve problems. In this article, we have used mathematical operations to evaluate the expression $4^3$.
• Mathematical Formulas Mathematical formulas, such as the formula for exponents, are used to simplify and evaluate mathematical expressions. In this article, we have used the formula for exponents to evaluate the expression $4^3$.

References

• Mathematics Handbook The mathematics handbook is a comprehensive reference book that covers various topics in mathematics, including exponents and powers.
• Mathematics Textbook The mathematics textbook is a comprehensive textbook that covers various topics in mathematics, including exponents and powers.
• Online Resources Online resources, such as websites and online tutorials, are available to provide additional information and support for learning mathematics.

Glossary

• Exponent: An exponent is a number that represents the power to which a base number is raised.
• Base: A base is a number that is raised to a power.
• Power: A power is a number that represents the exponent to which a base number is raised.
• Rule of Exponents: The rule of exponents states that $a^b \times a^c = a^{b+c}$.
• Property of Exponents: The property of exponents states that $a^m \times a^n = a^{m+n}$.
• Formula for Exponents: The formula for exponents states that $a^b = a \times a \times ... \times a$ (b times).