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Chapter 1: Problem 29

\((-10)^{2}\)

Short Answer

Expert verified
100

Step by step solution

01

Identify the Base and Exponent

The given expression is \((-10)^2\). Here, -10 is the base and 2 is the exponent.
02

Apply the Exponent

To simplify \((-10)^2\), you need to multiply the base (-10) by itself as many times as the exponent. In this case, you need to multiply -10 by itself 2 times.
03

Calculate the Multiplication

Calculate \((-10) \times (-10) \). Multiplying two negative numbers results in a positive number. So the calculation is \(-10 \times -10 = 100\).
04

Write Down the Final Answer

After performing the multiplication, the result is 100. Therefore, \((-10)^2 = 100\).

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Key Concepts

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

Understanding Base and Exponent
In mathematics, exponents are used to represent repeated multiplication of the same number. An exponent consists of two parts: the 'base' and the 'exponent'. The base is the number being multiplied, and the exponent tells you how many times to multiply the base by itself.
For example, in the expression \((-10)^2\), \-10\ is the base and 2 is the exponent. This means \(-10\) is to be multiplied by itself two times, like this: \(-10 \times -10\).
Multiplying Negative Numbers
Multiplying negative numbers can sometimes seem confusing, but it's straightforward once you know the rules. When you multiply two negative numbers, the result is always a positive number.
This is because each negative sign essentially 'cancels out' the other.
For instance, if you multiply \(-10 \times -10\), you get 100.
  • The first negative sign means 'opposite of 10'.
  • The second negative sign turns it back around to 'opposite of the opposite of 10', which is positive 10.

So, \(-10 \times -10 = 100\).
Squaring a Number
When we 'square' a number, we are raising it to the power of two. This means multiplying the number by itself.
In the case of negative numbers, squaring them follows the same rule, but as we learned earlier, multiplying two negative numbers gives a positive result.
For example, if you square \(-10\), you calculate \(-10 \times -10 \). This gives us 100.
  • Start by writing down the expression: \((-10)^2\)
  • Next, calculate the multiplication: \(-10 \times -10\)
  • The final result will be 100.

So, \((-10)^2 = 100\).

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Most popular questions from this chapter

Evaluate \(12 \mathrm{~kg}+54 \mathrm{~g}\). Write the answer in kilograms.

Find the circumference of a circle with a diameter of \(6 \mathrm{~cm}\).

Problem: Complete the "Understand the problem," "Make a plan," and "Complete the plan" steps. The regular price of a 12 -cup programmable coffee maker is \(\$ 79.99\). The sale price is \(\$ 59.99\). Find the percent discount. Round to the nearest percent. Incorrect Answer: The unknown is the percent discount; \(P=\) percent discount. A word equation is percent decrease \(=\left(\frac{\text { decrease in price }}{\text { sale price }}\right)(100) \%\). $$ \begin{aligned} &P=\left(\frac{\$ 79.99-\$ 59.99}{\$ 59.99}\right)(100) \% \\ &P=33 \% \text { decrease } \end{aligned} $$

The regular price of an elliptical trainer is \(\$ 899.99\). It is marked down \(18 \%\). The sales tax is \(7.4 \%\). Find the final cost of the elliptical trainer including tax. Round to the nearest hundredth.

Explain why \(\sqrt{25}\) does not equal \(-5\) even though \((-5)(-5)=25 .\)
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