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Chapter 10: Problem 74

Simplify. $$ -9^{2}-11 $$

Short Answer

Expert verified
The simplified value is $$-92$$.

Step by step solution

01

Apply Exponent

First, calculate the square of \(9^2\). This gives us: $$9^2 = 81$$. Now substitute this back into the expression: $$ -9^2 - 11 = -81 - 11$$.
02

Combine like terms

Next, perform the subtraction: $$-81 - 11 = -92$$.

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Key Concepts

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

Exponents
Exponents are a way to represent repeated multiplication. For example, the expression \(9^2\) means multiplying 9 by itself: 9 * 9. In our exercise, we simplify the exponent first by calculating \(9^2\), which equals 81. This simplification step is crucial and must be done before addressing any other parts of the expression.
Exponents are part of the order of operations rules, often memorized as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Following this order ensures we arrive at the correct answer. Ignoring the order can lead to very different and incorrect results.
Simplifying Expressions
Simplifying expressions involves performing all necessary operations in the correct sequence to reduce the expression to its simplest form. In our case, the expression \(-9^2 - 11\) requires us to first compute the exponent, which we did in the first section.
Then, we substitute \(81\) back into the expression, making it \(-81 - 11\). Simplification is about making expressions easier to understand and use by performing the basic arithmetic operations as prescribed by the order of operations.
Think of it as cleaning up and organizing a mess of numbers and operations until only one number remains.
Subtraction
Subtraction is one of the basic arithmetic operations and involves taking one number away from another. In the exercise, after simplifying the exponent, we were left with \(-81 - 11\). Performing the subtraction operation, \(-81 - 11\), involves starting from -81 and taking away 11.
It's helpful to think of subtraction on a number line: starting at -81 and moving 11 steps more to the left, which lands us at -92. Always align your subtraction process according to the order of operations to avoid mistakes and ensure accurate results.

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