Problem 30 Simplify using the order of oper... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 30

Simplify using the order of operations. $$6^{2}-(-4)^{2}$$

Short Answer

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Step by step solution

Identify the operations

The expression to simplify is \[ 6^{2} - (-4)^{2} \]Identify the operations involved: exponentiation and subtraction.

Simplify the exponents

Calculate each exponent separately. First, find \[ 6^{2} = 6 \times 6 = 36 \]Then find \[ (-4)^{2} = (-4) \times (-4) = 16 \]Now, substitute these values back into the expression, which results in \[ 36 - 16 \]

Perform the subtraction

Finally, subtract the numbers: \[ 36 - 16 = 20 \]

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Key Concepts

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

Exponentiation

Exponentiation is an important part of order of operations in mathematics. It tells you to multiply a number by itself a certain number of times. For example, in the expression $6^2$, the base number is 6, and the exponent is 2. This means you multiply 6 by itself:

$6 \times 6 = 36$

Similarly, for $(-4)^2$, the base is -4 and the exponent is 2. This means:

$(-4) \times (-4) = 16$

Note that when you square a negative number, you multiply the negative number by itself, resulting in a positive product.

Simplifying Expressions

Simplifying expressions involves performing operations in the correct order to reduce the expression to its simplest form. First, follow the order of operations, which is often remembered by the acronym PEMDAS:

P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction

In the given exercise, you need to handle exponentiation before moving on to other operations. Calculate the exponents $6^2$ and $(-4)^2$ first:

$6^2 = 36$
$(-4)^2 = 16$

Now replace the original numbers with their calculated values to simplify the subtraction in the next step.

Subtraction

Subtraction is one of the basic arithmetic operations, and it comes last in the order of operations for this particular problem. After you simplify the exponents, you end up with the subtraction expression $36 - 16$.

Simply subtract 16 from 36:

$36 - 16 = 20$

You've now completed all steps according to the order of operations, resulting in the simplified expression. In this case, the final answer is 20.

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91影视

Simplify using the order of operations. $$6^{2}-(-4)^{2}$$

Short Answer

Step by step solution

Identify the operations

Simplify the exponents

Perform the subtraction

Key Concepts

Exponentiation

Simplifying Expressions

Subtraction

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