Problem 60 Simplify. $$ \begin{array}{l... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 60

Simplify. $$ \begin{array}{l} 4^{3}+10 \cdot 20+ \\ 8^{2}-23 \end{array} $$

Short Answer

Expert verified

305

Step by step solution

Calculate the exponents

First, compute the values of the expressions with exponents. Simplify them to: - Calculate $4^3$ which is $4 \times 4 \times 4 = 64$ - Calculate $8^2$ which is $8 \times 8 = 64$

Perform the multiplication

Next, perform the multiplication: - Calculate $10 \times 20$ which equals $200$

Add and subtract the results

Now add and subtract the numbers obtained from previous steps in the following order: - Start with the sum of exponents and multiplication result: $64 + 200 + 64$ - Simplify this to $328$ - Subtract $23$ from $328$ to get the final result: $328 - 23 = 305$

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Key Concepts

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

Exponents

Exponents are a way of expressing repeated multiplication of the same number. They are written in the form of a base number raised to a power. For instance, in the expression $4^3$, the base is 4 and the exponent (or power) is 3.
This means multiplying 4 by itself three times: $4 \times 4 \times 4 = 64$.
Similarly, in the expression $8^2$, the base is 8 and the exponent is 2, which means $8 \times 8 = 64$.
The key point to remember is to always calculate the values of exponents before moving on to other operations in a mathematical expression.

Multiplication

Multiplication is a basic arithmetic operation that involves calculating the product of two numbers. For example, in the expression $10 \times 20$, we multiply 10 by 20 to get 200.
When working through an expression with multiple steps, it's essential to follow the order of operations. This means calculating exponents first (if any), followed by multiplication and division from left to right.

Addition and Subtraction

Addition and subtraction are basic arithmetic operations that are usually performed after exponents and multiplication. They involve combining values (in the case of addition) or finding the difference between values (in the case of subtraction).
In our example expression, once the exponents and multiplication have been calculated, we move on to adding and subtracting the results:
- First, add the results of the exponents and multiplication: $64 + 200 +64 = 328$
- Then subtract 23 from 328 to get the final result: $328 - 23 = 305$.
Following this order ensures you simplify the expression correctly and accurately.

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91影视

Simplify. $$ \begin{array}{l} 4^{3}+10 \cdot 20+ \\ 8^{2}-23 \end{array} $$

Short Answer

Step by step solution

Calculate the exponents

Perform the multiplication

Add and subtract the results

Key Concepts

Exponents

Multiplication

Addition and Subtraction

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