Problem 69 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 69

In the following exercises, simplify each expression with exponents. $$-0.5^{2}$$

Short Answer

Expert verified

-0.25

Step by step solution

Understand the expression

The given expression is -0.5^{2}. It implies a negative sign outside the squared base 0.5. Thus you need to first calculate the square of 0.5 and then apply the negative sign.

Square the base

Calculate the square of 0.5: (0.5)^{2} = 0.25

Apply the negative sign

Now apply the negative sign to the result. - (0.25) = -0.25

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Key Concepts

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

negative exponents

Negative exponents can seem tricky at first, but they actually follow a simple rule. When you see a negative exponent, it means you take the reciprocal of the base and then apply the positive exponent. For example, let's consider the expression $(2)^{-3}$. Here is the step-by-step solution:

Step 1: Take the reciprocal of the base. The base is 2, so the reciprocal is $\frac{1}{2}$.
Step 2: Apply the positive exponent: $(\frac{1}{2})^{3} = \frac{1}{8}$.

This means $(2)^{-3} = \frac{1}{8}$
Negative exponents do not mean negative numbers, but rather fractions.

squaring numbers

Squaring a number means multiplying it by itself. It's an important concept in mathematics and appears in many areas such as algebra, geometry, and calculus. To square a number, bear in mind the following:

Start with a base number, let's say 4.
Multiply it by itself: $4 \times 4$.
The result is $16$, so $4^{2} = 16$.

For our specific exercise, squaring $0.5$:

Step 1: Multiply $0.5 \times 0.5$.
Step 2: Get the result $0.25$.

So, $0.5^{2} = 0.25$. Squaring works the same way for positive, negative, and fractional numbers!

order of operations

The order of operations is crucial in solving mathematical expressions correctly. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)), this rule tells us the sequence in which to solve parts of a math problem.

For example, in the expression $-0.5^{2}$:

Step 1: Calculate the exponent, $0.5^{2} = 0.25$.
Step 2: Apply the negative sign afterward, resulting in $-0.25$.

If you do not follow the order of operations, you could get a completely wrong answer. Always start with parentheses, then move to exponents before handling multiplication, division, addition, and subtraction in that order!

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91影视

In the following exercises, simplify each expression with exponents. $$-0.5^{2}$$

Short Answer

Step by step solution

Understand the expression

Square the base

Apply the negative sign

Key Concepts

negative exponents

squaring numbers

order of operations

One App. One Place for Learning.

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