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Chapter 1: Problem 43

Simplify. $$ 5 \cdot 3^{2}-4^{2} \cdot 2 $$

Short Answer

Expert verified
13

Step by step solution

01

Evaluate Exponents

First, find the value of the exponents. Calculate \(3^{2}\) and \(4^{2}\). \(3^{2} = 9\) and \(4^{2} = 16\)
02

Multiply

Next, perform the multiplication in the expression. \(5 \times 9 = 45\) and \(16 \times 2 = 32\)
03

Subtract

Finally, perform the subtraction to simplify the expression. \(45 - 32 = 13\)

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Key Concepts

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

Exponents
When simplifying expressions, evaluating exponents is one of the first steps. Exponents represent how many times a number, known as the base, is multiplied by itself. For example, in the expression \(3^2\), 3 is the base and 2 is the exponent. This means you multiply 3 by itself: \(3 \times 3 = 9\). Similarly, for \(4^2\), you calculate \(4 \times 4 = 16\). It's crucial to handle exponents correctly to get accurate results in your calculations.
Multiplication
Once you've evaluated the exponents in an expression, the next step is to perform the multiplication. In our example, we have two multiplications to do: \(5 \times 9\) and \(4^2 \times 2\). From the previous step, we know \(3^2 = 9\) and \(4^2 = 16\). So we multiply these results by the remaining numbers. For \(5 \times 9\), the result is 45. For \(16 \times 2\), the result is 32. Always perform multiplication from left to right and ensure each step is accurate to avoid errors.
Subtraction
With the product results ready, the final step is to subtract the second product from the first. From the multiplication, we have 45 and 32. So, the final task is to calculate \(45 - 32\). Subtraction can be thought of as taking away a certain number from another. In our case, subtract 32 from 45 to get 13. Subtraction is often the last step in simplifying expressions if it's the only operation left.

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Most popular questions from this chapter

If \(n>0, m>0,\) and \(n \neq m,\) classify each of the following as either true or false. $$ m-n=-(n-m) $$

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