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Chapter 6: Problem 50

Simplify each expression. Write answers using positive exponents. $$ -3 s^{0} t $$

Short Answer

Expert verified
The simplified expression is \(-3t\).

Step by step solution

01

Evaluate the Zero Exponent

Recall that any non-zero number raised to the power of zero is 1. Given the expression \(-3 s^{0} t\), we evaluate \(s^{0}\), which results in 1. Thus, the expression simplifies to \(-3 \times 1 \times t\), simplifying further to just \(-3t\).
02

Final Simplification

The expression from Step 1 is \(-3t\). It is already in its simplest form because all exponents are positive, and there are no like terms to combine. Thus, the simplified expression is \(-3t\).

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Key Concepts

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

Zero Exponent Rule
The zero exponent rule is a fundamental concept in algebra that states any non-zero number raised to the power of zero equals one. This rule helps simplify expressions involving exponents, making them easier to work with.
For example, in the expression \(s^{0}\), applying the zero exponent rule tells us that \(s^{0} = 1\). It doesn't matter what the base of the exponent is鈥攁s long as it is not zero, the result will always be one!
This rule simplifies expressions and reduces complexity, forming the basis for understanding more advanced exponent operations.
Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form. This process often includes combining like terms, applying mathematical rules like the zero exponent rule, and converting all exponents to positive values.
In the given problem, after applying the zero exponent rule to \(s^{0}\), the expression becomes \(-3 \times 1 \times t\). This can be simplified to \(-3t\).
Simplifying an expression ensures that it is as concise as possible, making it easier to understand and use in equations or further calculations.
Positive Exponents
When simplifying, it's important to write expressions using positive exponents. Positive exponents indicate standard multiplication rather than division or other operations.
In some cases, if you end up with negative exponents, they need to be rewritten as positive exponents. But for the expression \(-3t\), notice that no negative exponents are present.
Using positive exponents keeps the expressions straightforward and prevents confusion, especially as you tackle more complex algebraic problems.

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Most popular questions from this chapter

Let \(Q(x)=x^{4}-3 x^{3}+2 x^{2}+x-3 .\) Evaluate \(Q(x)\) by substituting the given value of \(x\) into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. See Example 4. $$ Q(3) $$

Use synthetic division to perform each division. $$ \left(x^{2}+13 x+42\right) \div(x+6) $$

Solve equation. If a solution is extraneous, so indicate. \(\frac{7}{5 x}-\frac{1}{2}=\frac{5}{6 x}+\frac{1}{3}\)

Use synthetic division to perform each division. $$ \left(t^{3}+t^{2}+t+2\right) \div(t+1) $$

When dividing a polynomial by a binomial of the form \(x-k\) synthetic division is considered to be faster than long division. Explain why.
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