Problem 50 Simplify. $$-4^{4}$$... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 2: Problem 50

Simplify. $$-4^{4}$$

Short Answer

Expert verified

-256.

Step by step solution

- Identify the exponentiation

Recognize that the expression is $-4^4$, where 4 is the base and 4 is the exponent.

- Apply the exponentiation

Calculate the value of 4 raised to the power of 4: \[ 4^4 = 4 \times 4 \times 4 \times 4 = 256. \]

- Apply the negative sign

Since the exponentiation is $-4^4$, the negative sign applies after the exponentiation. Therefore, multiply -1 by the result: $-1 \times 256 = -256. $

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Key Concepts

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

Understanding Exponentiation

Exponentiation is a mathematical operation involving two numbers: the base and the exponent. The base is the number being multiplied, and the exponent shows how many times the base is used as a factor.
For example, in the expression $4^4$, the base is 4, and the exponent is 4. This means you multiply 4 by itself 4 times:
$4^4 = 4 \times 4 \times 4 \times 4 = 256$.
Understanding this concept is essential for simplifying expressions.

Working with Negative Numbers

When dealing with negative numbers, it's important to recognize their impact on mathematical operations. For instance, a negative sign before an exponent expression means you need to consider the order in which operations are performed.
In the exercise, the expression $-4^4$ involves calculating the exponentiation first, and then applying the negative sign.
This is because the negative sign is not part of the base in this case; it's outside the exponentiation operation.

Order of Operations

The order of operations is a fundamental concept in mathematics that dictates the sequence in which mathematical operations should be performed to ensure accurate results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), this rule guides us through complex expressions.
In the expression $-4^4$, exponentiation is performed before applying the negative sign. First, calculate $4^4$ to get 256. Then, apply the negative sign to get the final answer of -256.
This ensures the operations are correctly prioritized and the right result is obtained.

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91影视

Simplify. $$-4^{4}$$

Short Answer

Step by step solution

- Identify the exponentiation

- Apply the exponentiation

- Apply the negative sign

Key Concepts

Understanding Exponentiation

Working with Negative Numbers

Order of Operations

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