Problem 50 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(-3t\).

Step 2: 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 \(-3t\).

Key Concepts

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—as 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.