Problem 53 Find the value of each expressio... [FREE SOLUTION]

Chapter 1: Problem 53

Find the value of each expression. $$ \frac{6\left(3^{2}-1\right)+8}{8-2^{2}} $$

Short Answer

Expert verified

The value of the expression is 14.

Step by step solution

- Simplify inside the parentheses

First, simplify the expression inside the parentheses. Calculate the exponentiation in the numerator: $ 3^2 = 9 $Now subtract 1 from 9: $ 9 - 1 = 8 $

- Multiply by 6 and add 8

Next, multiply the result by 6 and add 8: $ 6 \times 8 = 48 $Now add 8 to 48: $ 48 + 8 = 56 $

- Simplify denominator

Simplify the denominator by calculating the exponentiation: $ 2^2 = 4 $Now subtract 4 from 8: $ 8 - 4 = 4 $

- Divide the results

Finally, divide the numerator by the denominator:$ \frac{56}{4} = 14 $

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations

When faced with a complex algebraic expression, it's essential to follow the order of operations. This order can be remembered with the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). For example, in the expression $\frac{6(3^2 鈭� 1) + 8}{8 鈭� 2^2}$, you start with the innermost parentheses.
You first handle the exponent within the parentheses, followed by subtraction. Next, you proceed with the multiplication and subsequently deal with any addition or subtraction, finally looking at the division.

Exponentiation

Exponentiation involves raising a number to the power of another number. It is a critical part of the order of operations and must be executed before other operations like multiplication or division.

In our example, we must calculate $3^2$ first, which equals 9.

Exponents indicate how many times to multiply the base number by itself. Hence, $3^2$ means $3 脳 3 = 9$. This simplifies the expression inside the parentheses before moving to the next part of the operation.

Fractions

Fractions represent a part of a whole and are composed of a numerator and a denominator. The numerator is the number above the fraction bar, while the denominator is below it.

To solve a fraction, you first need to simplify both the numerator and the denominator. Then, perform the division to find the final value.

In the given problem, the simplified numerator is 56 and the simplified denominator is 4, resulting in $\frac{56}{4} = 14$. This method of breaking down fractions into simpler parts makes them easier to solve.

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91影视

Find the value of each expression. $$ \frac{6\left(3^{2}-1\right)+8}{8-2^{2}} $$

Short Answer

Step by step solution

- Simplify inside the parentheses

- Multiply by 6 and add 8

- Simplify denominator

- Divide the results

Key Concepts

Order of Operations

Exponentiation

Fractions

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