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Chapter 0: Problem 1

Evaluate each exponential expression $$5^{2} \cdot 2$$

Short Answer

Expert verified
The result of the calculation \(5^{2} \cdot 2\) is 50

Step by step solution

01

Evaluate the exponent

First, evaluate the exponential part \(5^{2}\). This means you multiply 5 by itself, which equals 25.
02

Multiply with 2

Next, multiply the result of the exponent calculation (25) with 2. So, \(25 \cdot 2 = 50\)

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Key Concepts

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

evaluating exponents
Exponents are a mathematical way to express repeated multiplication. When you see an exponent, such as \(5^{2}\), it tells us to multiply the base number (in this case, 5) by itself. Therefore, \(5^{2}\) is read as "5 squared," meaning you multiply 5 by 5.

To evaluate \(5^{2}\):
  • Identify the base: here, the base is 5.
  • Identify the exponent: here, the exponent is 2.
  • Multiply the base by itself according to the exponent. Multiply 5 by 5 which results in 25.
This simple comprehension of evaluating exponents makes handling more complex expressions much easier.
multiplication
Once you've evaluated the exponent, the next step involves multiplication. In this exercise, we evaluated \(5^{2}\) to get 25. The problem then requires you to multiply 25 by 2.

Here's how to think about the multiplication process:
  • Write down your result from the exponent: 25
  • Identify the number you need to multiply with: 2
  • Perform the multiplication: 25 times 2 is 50
Remember, multiplication is combining groups of equal sizes. Here, you are adding two groups of 25, which gives you the final answer of 50.
step-by-step solutions
When it comes to solving mathematical expressions, breaking down each step is crucial for understanding. The step-by-step solution to the exercise highlights the importance of tackling one part of the problem before moving to the next.

Following the outlined steps ensures you don't miss any important details.
  • Step 1 involves evaluating the exponent: You dealt with \(5^{2}\) by multiplying 5 by itself.
  • Step 2 is about multiplying the result: You took the result, 25, and multiplied it by 2 to find the answer.
Taking problems one step at a time allows you to see the calculation process clearly and effectively. Such a methodical approach turns what might seem complex into a simple sequence of instructions.

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I evaluated \(\frac{3 x-3}{4 x(x-1)}\) for \(x=1\) and obtained 0.

Will help you prepare for the material covered in the next section. If the width of a rectangle is represented by \(x\) and the length is represented by \(x+200\), write a simplified algebraic expression that models the rectangle's perimeter.

The average rate on a round-trip commute having a one-way distance \(d\) is given by the complex rational expression $$\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$$ in which \(r_{1}\) and \(r_{2}\) are the average rates on the outgoing and return trips, respectively. Simplify the expression. Then find your average rate if you drive to campus averaging 40 miles per hour and return home on the same route averaging 30 miles per hour. Explain why the answer is not 35 miles per hour.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$
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