Combining the simplified parts

Oct 13, 2025 by magicalceylontours.com 112 views

Introduction

In this article, we will simplify each part of the given expression using the laws of exponents. We will also identify the laws or properties used to simplify each part and find the value of the expression.

The Expression

The given expression is:

$\frac{2^7}{2^5} + \left(4^5\right)^0 + 3^{-1}$

Simplifying each part

Part 1: $\frac{2^7}{2^5}$

To simplify this part, we will use the Quotient of Powers Property, which states that:

$\frac{a^m}{a^n} = a^{m-n}$

where $a$ is a non-zero number and $m$ and $n$ are integers.

Using this property, we can simplify the expression as follows:

$\frac{2^7}{2^5} = 2^{7-5} = 2^2$

Therefore, the simplified form of the first part is $2^2$ .

Part 2: $\left(4^5\right)^0$

To simplify this part, we will use the Zero Exponent Property, which states that:

$a^0 = 1$ for any non-zero number $a$ .

Using this property, we can simplify the expression as follows:

$\left(4^5\right)^0 = 1$

Therefore, the simplified form of the second part is $1$ .

Part 3: $3^{-1}$

To simplify this part, we will use the Negative Exponent Property, which states that:

$a^{-n} = \frac{1}{a^n}$

where $a$ is a non-zero number and $n$ is a positive integer.

Using this property, we can simplify the expression as follows:

$3^{-1} = \frac{1}{3^1} = \frac{1}{3}$

Therefore, the simplified form of the third part is $\frac{1}{3}$ .

Combining the simplified parts

Now that we have simplified each part, we can combine them to find the value of the expression:

$2^2 + 1 + \frac{1}{3}$

To add these terms, we need to find a common denominator, which is $3$ . We can rewrite the terms as follows:

$\frac{4}{1} + \frac{3}{3} + \frac{1}{3}$

Now we can add the terms:

$\frac{4}{1} + \frac{3}{3} + \frac{1}{3} = \frac{12}{3} + \frac{3}{3} + \frac{1}{3} = \frac{16}{3}$

Therefore, the value of the expression is $\frac{16}{3}$ .

Conclusion

$In this article, we simplified each part of the given expression using the laws of exponents. We identified the laws or properties used to simplify each part and found the value of the expression. The laws or properties used to simplify each part were the Quotient of Powers Property, the Zero Exponent Property, and the Negative Exponent Property. The value of the expression is $\frac{16}{3}$.<br/> **Simplify each part of the expression using the laws of exponents: Q&A**$

Introduction

In our previous article, we simplified each part of the given expression using the laws of exponents. We identified the laws or properties used to simplify each part and found the value of the expression. In this article, we will answer some frequently asked questions related to the simplification of the expression.

Q&A

Q: What is the Quotient of Powers Property?

A: The Quotient of Powers Property is a property of exponents that states that:

$\frac{a^m}{a^n} = a^{m-n}$

where $a$ is a non-zero number and $m$ and $n$ are integers.

Q: What is the Zero Exponent Property?

A: The Zero Exponent Property is a property of exponents that states that:

$a^0 = 1$ for any non-zero number $a$ .

Q: What is the Negative Exponent Property?

A: The Negative Exponent Property is a property of exponents that states that:

$a^{-n} = \frac{1}{a^n}$

where $a$ is a non-zero number and $n$ is a positive integer.

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

A: To simplify an expression with a negative exponent, you can use the Negative Exponent Property. For example, if you have the expression $3^{-1}$ , you can simplify it as follows:

$3^{-1} = \frac{1}{3^1} = \frac{1}{3}$

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

A: To simplify an expression with a zero exponent, you can use the Zero Exponent Property. For example, if you have the expression $\left(4^5\right)^0$ , you can simplify it as follows:

$\left(4^5\right)^0 = 1$

Q: What is the value of the expression $\frac{2^7}{2^5} + \left(4^5\right)^0 + 3^{-1}$ ?

A: The value of the expression is $\frac{16}{3}$ .

Q: What laws or properties did you use to simplify each part of the expression?

A: We used the Quotient of Powers Property, the Zero Exponent Property, and the Negative Exponent Property to simplify each part of the expression.

Q: Can you give an example of how to use the Quotient of Powers Property?

A: Yes, here is an example:

$\frac{2^7}{2^5} = 2^{7-5} = 2^2$

Q: Can you give an example of how to use the Zero Exponent Property?

A: Yes, here is an example:

$\left(4^5\right)^0 = 1$

Q: Can you give an example of how to use the Negative Exponent Property?

A: Yes, here is an example:

$3^{-1} = \frac{1}{3^1} = \frac{1}{3}$

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the expression using the laws of exponents. We hope that this article has been helpful in clarifying any doubts you may have had. If you have any further questions, please don't hesitate to ask.

Additional Resources

Practice Problems

Simplify the expression $\frac{3^7}{3^5} + \left(2^3\right)^0 + 4^{-1}$ .
Simplify the expression $\frac{5^8}{5^4} + \left(3^2\right)^0 + 2^{-1}$ .
Simplify the expression $\frac{2^9}{2^6} + \left(4^4\right)^0 + 3^{-1}$ .

We hope that these practice problems will help you to reinforce your understanding of the laws of exponents.