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Chapter 10: Problem 29

Simplify. $$3-n^{0}$$

Short Answer

Expert verified
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Step by step solution

01

- Identify the Exponent Rule

Understand that any number raised to the power of zero is equal to one. In this case, ^{0} = 1.
02

- Substitute and Simplify

Replace n^{0} with 1 in the given expression. So the expression becomes 3 - 1.
03

- Simplify the Expression

Perform the subtraction operation. 3 - 1 equals 2.

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Key Concepts

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

Zero Exponent Explained
The zero exponent rule is handy in algebra. Simply put, any number or variable raised to the power of zero equals one.

For example, in the expression given in the exercise, when we have \(n^{0}\), it means we need to replace it with 1.

This rule holds true for any non-zero number or variable. So, whether it鈥檚 \(5^{0}\), \(100^{0}\), or even \((x+y)^{0}\) 鈥� they all equal 1.

Understanding the zero exponent rule is crucial as it often appears in simplifying algebraic expressions.
Simplifying Expressions
Simplifying expressions means making them easier to understand or solve. For instance, an expression like the one in the problem \(3 - n^{0}\) can be simplified using the zero exponent rule.

Here are a few tips to simplify expressions:
  • Identify parts of the expression you can transform, such as exponents, coefficients, and like terms.
  • Substitute values where possible, as we did by replacing \(n^{0}\) with 1.
  • Perform basic arithmetic operations like addition, subtraction, multiplication, and division systematically.
This way, you make the expression simpler and easier to work with.
Subtraction in Algebra
In the exercise, we simplified the expression \(3 - n^{0}\) to 2 by performing a subtraction operation. Subtraction is a fundamental operation in algebra.

Here鈥檚 how it works:
  • First, identify the values you need to subtract.
  • Perform the subtraction operation. In our example, it was \(3 - 1 = 2\).
Remember: when you subtract, the order matters. Subtracting 5 from 3 is different from subtracting 3 from 5. So, always pay attention to the signs and order of terms in your expression.

With these basics, you鈥檒l be better equipped to handle algebraic expressions involving subtraction.

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Most popular questions from this chapter

Subtract the polynomials. $$\left(-19 a^{5}-6 a^{3}+2 a^{2}+7\right)-\left(4 a^{5}+2 a^{3}+6 a^{2}-3\right)$$

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Evaluate the polynomial for the given values of the variable. \(t^{2}-6 t-1\) a. for \(t=-2\) b. for \(t=\frac{1}{4}\)

Simplify the expression. $$\left(\frac{z}{2}\right)^{3}$$

Subtract the polynomials. $$\left(9 p^{3}-4 p^{2}+2 p\right)-\left(2 p^{3}+6 p^{2}-3 p\right)$$
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