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Chapter 0: Problem 112

For exercises 97-114, evaluate. $$ -18-100\left(\frac{1}{5}\right)^{2}-30 $$

Short Answer

Expert verified
-52

Step by step solution

01

Evaluate the exponent

First, evaluate the exponent part of the expression. Calculate \(\frac{1}{5}\) raised to the power of 2: \[ \left( \frac{1}{5} \right)^{2} = \frac{1}{25} \]
02

Multiply by -100

Next, multiply \( \frac{1}{25} \) by -100: \[ -100 \times \frac{1}{25} = -4 \]
03

Simplify the expression

Now, add and subtract the remaining terms in the expression: \[ -18 - 4 - 30 = -52 \]

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Key Concepts

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

Understanding Exponents
Exponents are a way of representing repeated multiplication of a number by itself. In our exercise, we have \(\frac{1}{5}\) raised to the power of 2. This means we multiply \(\frac{1}{5}\) by itself: \(\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}\). Exponents make calculations simpler and quicker by using this shorthand representation. Remember, the number being multiplied is called the 'base', and the exponent shows how many times to use the base in multiplication.
Multiplication of Fractions and Numbers
When multiplying fractions and numbers, it might seem tricky at first. In the given exercise, after calculating the exponent, we multiply \(-100\) by \(\frac{1}{25}\). Here's how you can think about it: \- Multiplying \(\frac{1}{25}\) by \(-100\) is the same as dividing \(-100\) by \(\frac{25}{1}\). \- \(\frac{-100 \times 1}{25 \times 1}\) simplifies to \-4 \. Always remember to keep track of the minus sign during multiplication. Cross-multiplication helps clear up any confusion.
Simplification of Expressions
Simplification makes expressions easier to handle by combining like terms and performing operations step-by-step. In our problem, after dealing with exponents and multiplication, we reduced terms: \- First, we calculated \(-18 - 4 - 30\)\. \- Start by combining \(-18 - 4 = -22\). \- Next, subtract \-30 from \-22, which results in \(-52\). Breaking down expressions into simpler parts helps in clear and accurate solutions. Always take one step at a time, and double-check each simplified part.

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Most popular questions from this chapter

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 18 \% $$

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$$ \text { Round } 0.2394 \text { to the nearest hundredth. } $$

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ \frac{5}{8} \quad \frac{2}{3} $$
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