Simplify The Expression:$\[ \frac{3}{4}(1+\sqrt{49})^2-(5-1)^3 \\]Choose The Correct Answer:A. 48 B. 44 C. -16 D. -36

Feb 28, 2025 by ADMIN 123 views

Simplify the Expression: A Step-by-Step Guide

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Introduction

In this article, we will simplify the given expression step by step. The expression is $\frac{3}{4}(1+\sqrt{49})^2-(5-1)^3$ . We will use basic algebraic operations and properties of exponents to simplify the expression.

Step 1: Simplify the Expression Inside the Parentheses

The expression inside the parentheses is $(1+\sqrt{49})$ . We can simplify this expression by evaluating the square root of 49.

$\sqrt{49} = 7$

So, the expression becomes $(1+7)$ .

$(1+7) = 8$

Step 2: Simplify the Expression Inside the Second Parentheses

The expression inside the second parentheses is $(5-1)$ . We can simplify this expression by subtracting 1 from 5.

$(5-1) = 4$

Step 3: Raise the Expression Inside the First Parentheses to the Power of 2

We need to raise the expression inside the first parentheses to the power of 2. This means we need to square the expression.

$(1+7)^2 = 8^2$

$8^2 = 64$

Step 4: Raise the Expression Inside the Second Parentheses to the Power of 3

We need to raise the expression inside the second parentheses to the power of 3. This means we need to cube the expression.

$(5-1)^3 = 4^3$

$4^3 = 64$

Step 5: Multiply the Expression Inside the First Parentheses by $\frac{3}{4}$

We need to multiply the expression inside the first parentheses by $\frac{3}{4}$ .

$\frac{3}{4}(1+7)^2 = \frac{3}{4}(64)$

$\frac{3}{4}(64) = 48$

Step 6: Subtract the Expression Inside the Second Parentheses from the Expression Inside the First Parentheses

We need to subtract the expression inside the second parentheses from the expression inside the first parentheses.

$\frac{3}{4}(1+7)^2 - (5-1)^3 = 48 - 64$

$48 - 64 = -16$

Conclusion

In this article, we simplified the given expression step by step. We used basic algebraic operations and properties of exponents to simplify the expression. The final answer is $\boxed{-16}$ .

Final Answer

The final answer is $\boxed{-16}$ .

Discussion

The discussion category for this article is mathematics. If you have any questions or need further clarification, please feel free to ask.

Simplifying Expressions with Exponents
Algebraic Operations and Properties
Mathematics Formulas and Equations

Author

The author of this article is [Your Name]. If you have any questions or need further clarification, please feel free to ask.

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Introduction

In our previous article, we simplified the given expression step by step. We used basic algebraic operations and properties of exponents to simplify the expression. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to evaluate any expressions inside parentheses. This means we need to simplify any expressions that are inside parentheses before we can simplify the rest of the expression.

Q: What is the order of operations when simplifying an expression?

A: The order of operations when simplifying an expression is:

Evaluate any expressions inside parentheses.
Evaluate any exponential expressions (e.g. 2^3).
Evaluate any multiplication and division operations from left to right.
Evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression with a square root?

A: To simplify an expression with a square root, we need to find the square root of the number inside the square root sign. For example, if we have the expression $\sqrt{16}$ , we can simplify it by finding the square root of 16, which is 4.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable. For example, in the expression 3x, 3 is the coefficient and x is the variable. A variable is a letter or symbol that represents a value that can change.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, we need to follow the order of operations. This means we need to evaluate any expressions inside parentheses, then evaluate any exponential expressions, then evaluate any multiplication and division operations from left to right, and finally evaluate any addition and subtraction operations from left to right.

Q: What is the final answer to the expression $\frac{3}{4}(1+\sqrt{49})^2-(5-1)^3$ ?

A: The final answer to the expression $\frac{3}{4}(1+\sqrt{49})^2-(5-1)^3$ is -16.

Q: Can you provide more examples of simplifying expressions?

A: Yes, here are a few more examples of simplifying expressions:

$\frac{2}{3}(x+5)^2 - (x-2)^3$
$\frac{1}{2}(3x-2)^2 + (2x+1)^3$
$\frac{3}{4}(x+2)^2 - (x-1)^3$

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We covered topics such as the order of operations, simplifying expressions with square roots, coefficients and variables, and fractions. We also provided some examples of simplifying expressions.

Final Answer

The final answer is $\boxed{-16}$ .

Discussion

The discussion category for this article is mathematics. If you have any questions or need further clarification, please feel free to ask.

Simplifying Expressions with Exponents
Algebraic Operations and Properties
Mathematics Formulas and Equations

Author

The author of this article is [Your Name]. If you have any questions or need further clarification, please feel free to ask.

Simplify The Expression:$\[ \frac{3}{4}(1+\sqrt{49})^2-(5-1)^3 \\]Choose The Correct Answer:A. 48 B. 44 C. -16 D. -36

Introduction

Step 1: Simplify the Expression Inside the Parentheses

Step 2: Simplify the Expression Inside the Second Parentheses

Step 3: Raise the Expression Inside the First Parentheses to the Power of 2

Step 4: Raise the Expression Inside the Second Parentheses to the Power of 3

Step 5: Multiply the Expression Inside the First Parentheses by $\frac{3}{4}$

Step 6: Subtract the Expression Inside the Second Parentheses from the Expression Inside the First Parentheses

Conclusion

Final Answer

Discussion

Related Articles

Tags

Author

Introduction

Q: What is the first step in simplifying an expression?

Q: What is the order of operations when simplifying an expression?

Q: How do I simplify an expression with a square root?

Q: What is the difference between a coefficient and a variable?

Q: How do I simplify an expression with a fraction?

Q: What is the final answer to the expression $\frac{3}{4}(1+\sqrt{49})^2-(5-1)^3$ ?

Q: Can you provide more examples of simplifying expressions?

Conclusion

Final Answer

Discussion

Related Articles

Tags

Author

Introduction

Step 1: Simplify the Expression Inside the Parentheses

Step 2: Simplify the Expression Inside the Second Parentheses

Step 3: Raise the Expression Inside the First Parentheses to the Power of 2

Step 4: Raise the Expression Inside the Second Parentheses to the Power of 3

Step 5: Multiply the Expression Inside the First Parentheses by 34\frac{3}{4}43​

Step 6: Subtract the Expression Inside the Second Parentheses from the Expression Inside the First Parentheses

Conclusion

Final Answer

Discussion

Related Articles

Tags

Author

Introduction

Q: What is the first step in simplifying an expression?

Q: What is the order of operations when simplifying an expression?

Q: How do I simplify an expression with a square root?

Q: What is the difference between a coefficient and a variable?

Q: How do I simplify an expression with a fraction?

Q: What is the final answer to the expression 34(1+49)2−(5−1)3\frac{3}{4}(1+\sqrt{49})^2-(5-1)^343​(1+49​)2−(5−1)3?

Q: Can you provide more examples of simplifying expressions?

Conclusion

Final Answer

Discussion

Related Articles

Tags

Author

Step 5: Multiply the Expression Inside the First Parentheses by $\frac{3}{4}$

Q: What is the final answer to the expression $\frac{3}{4}(1+\sqrt{49})^2-(5-1)^3$ ?