Geoffrey Is Evaluating The Expression ( − 3 ) 3 ( 2 6 ) ( − 3 ) 5 ( 2 2 ) \frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)} ( − 3 ) 5 ( 2 2 ) ( − 3 ) 3 ( 2 6 ) ​ As Shown Below: ( − 3 ) 3 ( 2 6 ) ( − 3 ) 5 ( 2 2 ) = ( 2 ) 2 ( − 3 ) B = C D \frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}=\frac{(2)^2}{(-3)^b}=\frac{c}{d} ( − 3 ) 5 ( 2 2 ) ( − 3 ) 3 ( 2 6 ) ​ = ( − 3 ) B ( 2 ) 2 ​ = D C ​ What Are The Values Of $a, B,

Introduction

In mathematics, evaluating expressions is a crucial skill that helps us simplify complex mathematical statements. In this article, we will focus on evaluating the expression $\frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}$ step by step. We will break down the expression into smaller parts, simplify each part, and then combine them to get the final result.

Breaking Down the Expression

The given expression is $\frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}$. To simplify this expression, we need to break it down into smaller parts. We can start by simplifying the exponents.

Simplifying Exponents

The expression contains two exponents: $(-3)^3$ and $(-3)^5$. We can simplify these exponents by applying the power rule of exponents, which states that $(a^m)^n = a^{mn}$.

import math
base = -3
exponent1 = 3
exponent2 = 5

simplified_exponent1 = base ** exponent1
simplified_exponent2 = base ** exponent2
print(f"Simplified exponent 1: simplified_exponent1}")
print(f"Simplified exponent 2 {simplified_exponent2")

Simplifying the Numerator and Denominator

Now that we have simplified the exponents, we can simplify the numerator and denominator separately.

The numerator is $(-3)^3\left(2^6\right)$. We can simplify this by multiplying the two terms.

# Define the numerator
numerator = (-3) ** 3 * (2 ** 6)
print(f"Numerator: {numerator}")

The denominator is $(-3)^5\left(2^2\right)$. We can simplify this by multiplying the two terms.

# Define the denominator
denominator = (-3) ** 5 * (2 ** 2)
print(f"Denominator: {denominator}")

Simplifying the Expression

Now that we have simplified the numerator and denominator, we can simplify the expression by dividing the numerator by the denominator.

# Simplify the expression
simplified_expression = numerator / denominator
print(f"Simplified expression: {simplified_expression}")

Simplifying the Expression Further

The simplified expression is $\frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}$. We can simplify this expression further by canceling out common factors.

Canceling Out Common Factors

The numerator and denominator have common factors: $(-3)^3$ and $(-3)^5$. We can cancel out these common factors by dividing both the numerator and denominator by $(-3)^3$.

# Cancel out common factors
canceled_numerator = numerator / ((-3) ** 3)
canceled_denominator = denominator / ((-3) ** 3)
print(f"Canceled numerator: canceled_numerator}")
print(f"Canceled denominator {canceled_denominator")

Simplifying the Expression

Now that we have canceled out the common factors, we can simplify the expression by dividing the numerator by the denominator.

# Simplify the expression
simplified_expression = canceled_numerator / canceled_denominator
print(f"Simplified expression: {simplified_expression}")

Conclusion

In this article, we evaluated the expression $\frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}$ step by step. We broke down the expression into smaller parts, simplified each part, and then combined them to get the final result. We also canceled out common factors to simplify the expression further.

Final Answer

The final answer is $\boxed{\frac{4}{27}}$.

Discussion

What are the values of $a, b, c, d$ in the expression $\frac{c}{d}=\frac{(2)^2}{(-3)^b}$?

The values of $a, b, c, d$ are:

• $a = 2$
• $b = 5$
• $c = 4$
• $d = 27$

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Introduction

In our previous article, we evaluated the expression $\frac{(-3)^3\left(2^6\right)}{(-3)^5\left(2^2\right)}$ step by step. We broke down the expression into smaller parts, simplified each part, and then combined them to get the final result. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

Q: What is the value of $a$ in the expression $\frac{c}{d}=\frac{(2)^2}{(-3)^b}$?

A: The value of $a$ is 2.

Q: What is the value of $b$ in the expression $\frac{c}{d}=\frac{(2)^2}{(-3)^b}$?

A: The value of $b$ is 5.

Q: What is the value of $c$ in the expression $\frac{c}{d}=\frac{(2)^2}{(-3)^b}$?

A: The value of $c$ is 4.

Q: What is the value of $d$ in the expression $\frac{c}{d}=\frac{(2)^2}{(-3)^b}$?

A: The value of $d$ is 27.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you can use the power rule of exponents, which states that $(a^m)^n = a^{mn}$. You can also cancel out common factors by dividing both the numerator and denominator by the common factor.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you can multiply the numerator and denominator by the same value to eliminate the fraction. You can also cancel out common factors by dividing both the numerator and denominator by the common factor.

Q: What is the difference between simplifying an expression and evaluating an expression?

A: Simplifying an expression involves reducing the expression to its simplest form, while evaluating an expression involves finding the value of the expression.

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the values of the variables into the expression and then simplify the expression.

Q: What are some common mistakes to avoid when evaluating expressions?

A: Some common mistakes to avoid when evaluating expressions include:

• Not simplifying the expression before evaluating it
• Not canceling out common factors
• Not using the correct order of operations
• Not substituting the values of variables correctly

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions. We covered topics such as simplifying expressions with exponents and fractions, evaluating expressions with multiple variables, and common mistakes to avoid. We hope that this article has been helpful in clarifying any confusion you may have had about evaluating expressions.

Final Answer

The final answer is $\boxed{\frac{4}{27}}$.

Discussion

Do you have any questions about evaluating expressions? Ask us in the comments below!