Simplify The Expression:$ (1.5)(1.5)^2 $

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Introduction

In mathematics, simplifying expressions is an essential skill that helps us solve problems more efficiently. When dealing with exponents, it's crucial to understand the rules of exponentiation to simplify expressions accurately. In this article, we will focus on simplifying the expression (1.5)(1.5)2(1.5)(1.5)^2 using the rules of exponentiation.

Understanding Exponents

Before we dive into simplifying the expression, let's briefly review the rules of exponentiation. An exponent is a small number that is placed above and to the right of a base number. It tells us how many times to multiply the base number by itself. For example, in the expression 232^3, the base number is 2 and the exponent is 3. This means we need to multiply 2 by itself 3 times: 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8.

Simplifying the Expression

Now that we have a basic understanding of exponents, let's simplify the expression (1.5)(1.5)2(1.5)(1.5)^2. To do this, we need to apply the rule of exponentiation that states when we multiply two numbers with the same base, we add their exponents. In this case, the base number is 1.5, and the exponents are 1 and 2.

Using the rule of exponentiation, we can rewrite the expression as:

(1.5)(1.5)2=(1.5)1×(1.5)2(1.5)(1.5)^2 = (1.5)^1 \times (1.5)^2

Applying the Rule of Exponentiation

Now that we have rewritten the expression, we can apply the rule of exponentiation to simplify it. When we multiply two numbers with the same base, we add their exponents. In this case, the exponents are 1 and 2, so we add them together:

(1.5)1×(1.5)2=(1.5)1+2(1.5)^1 \times (1.5)^2 = (1.5)^{1+2}

Simplifying the Exponent

Now that we have added the exponents, we can simplify the expression further by evaluating the new exponent. In this case, the new exponent is 3, so we can rewrite the expression as:

(1.5)1+2=(1.5)3(1.5)^{1+2} = (1.5)^3

Evaluating the Expression

Now that we have simplified the expression, we can evaluate it by multiplying 1.5 by itself 3 times:

(1.5)3=1.5×1.5×1.5=3.375(1.5)^3 = 1.5 \times 1.5 \times 1.5 = 3.375

Conclusion

In this article, we simplified the expression (1.5)(1.5)2(1.5)(1.5)^2 using the rules of exponentiation. We started by understanding the rules of exponentiation, then applied the rule of exponentiation to simplify the expression, and finally evaluated the expression to get the final answer. By following these steps, we can simplify expressions with exponents accurately and efficiently.

Frequently Asked Questions

  • What is the rule of exponentiation? The rule of exponentiation states that when we multiply two numbers with the same base, we add their exponents.
  • How do we simplify expressions with exponents? To simplify expressions with exponents, we need to apply the rule of exponentiation, which states that when we multiply two numbers with the same base, we add their exponents.
  • What is the final answer to the expression (1.5)(1.5)2(1.5)(1.5)^2? The final answer to the expression (1.5)(1.5)2(1.5)(1.5)^2 is 3.375.

Additional Resources

  • Khan Academy: Exponents and Exponential Functions
  • Mathway: Exponent Rules
  • Wolfram Alpha: Exponentiation

Final Thoughts

Simplifying expressions with exponents is an essential skill in mathematics that helps us solve problems more efficiently. By understanding the rules of exponentiation and applying them accurately, we can simplify expressions with exponents and get the final answer. In this article, we simplified the expression (1.5)(1.5)2(1.5)(1.5)^2 using the rules of exponentiation, and we hope that this article has provided you with a better understanding of how to simplify expressions with exponents.

Introduction

In our previous article, we simplified the expression (1.5)(1.5)2(1.5)(1.5)^2 using the rules of exponentiation. In this article, we will answer some frequently asked questions related to simplifying expressions with exponents.

Q&A

Q: What is the rule of exponentiation?

A: The rule of exponentiation states that when we multiply two numbers with the same base, we add their exponents.

Q: How do we simplify expressions with exponents?

A: To simplify expressions with exponents, we need to apply the rule of exponentiation, which states that when we multiply two numbers with the same base, we add their exponents.

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

A: A base is the number that is being multiplied by itself, and an exponent is the number that tells us how many times to multiply the base by itself.

Q: Can we simplify expressions with negative exponents?

A: Yes, we can simplify expressions with negative exponents by applying the rule of exponentiation. When we have a negative exponent, we can rewrite it as a positive exponent by flipping the base and changing the sign of the exponent.

Q: How do we simplify expressions with fractional exponents?

A: To simplify expressions with fractional exponents, we need to apply the rule of exponentiation, which states that when we multiply two numbers with the same base, we add their exponents. We also need to use the property of fractional exponents, which states that am/n=amna^{m/n} = \sqrt[n]{a^m}.

Q: Can we simplify expressions with zero exponents?

A: Yes, we can simplify expressions with zero exponents by applying the rule of exponentiation. When we have a zero exponent, the expression is equal to 1.

Q: How do we simplify expressions with negative bases?

A: To simplify expressions with negative bases, we need to apply the rule of exponentiation, which states that when we multiply two numbers with the same base, we add their exponents. We also need to use the property of negative bases, which states that (−a)n=an(-a)^n = a^n if n is even and (−a)n=−an(-a)^n = -a^n if n is odd.

Q: Can we simplify expressions with complex numbers?

A: Yes, we can simplify expressions with complex numbers by applying the rule of exponentiation and using the properties of complex numbers.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions with exponents. We hope that this article has provided you with a better understanding of how to simplify expressions with exponents and has helped you to answer some of the most common questions related to this topic.

Frequently Asked Questions

  • What is the rule of exponentiation?
  • How do we simplify expressions with exponents?
  • What is the difference between a base and an exponent?
  • Can we simplify expressions with negative exponents?
  • How do we simplify expressions with fractional exponents?
  • Can we simplify expressions with zero exponents?
  • How do we simplify expressions with negative bases?
  • Can we simplify expressions with complex numbers?

Additional Resources

  • Khan Academy: Exponents and Exponential Functions
  • Mathway: Exponent Rules
  • Wolfram Alpha: Exponentiation

Final Thoughts

Simplifying expressions with exponents is an essential skill in mathematics that helps us solve problems more efficiently. By understanding the rules of exponentiation and applying them accurately, we can simplify expressions with exponents and get the final answer. In this article, we answered some frequently asked questions related to simplifying expressions with exponents, and we hope that this article has provided you with a better understanding of how to simplify expressions with exponents.