Simplify. Express your answer as a single term: s^{-1} t^{0} imes st.
Understand the Problem
The question is asking to simplify the expression given, which includes variables raised to powers. The goal is to combine like terms and present the result in a simplified form.
Answer
The simplified expression is $t$.
Answer for screen readers
The simplified expression is $t$.
Steps to Solve
- Identify the Expression
The given expression is: $$ s^{-1} t^{0} \cdot s t $$
- Simplify Powers of Variables
Recall that any variable to the power of zero is equal to 1. Therefore: $$ t^{0} = 1 $$ Substituting this in, the expression simplifies to: $$ s^{-1} \cdot 1 \cdot s t = s^{-1} s t $$
- Combine Like Terms
Using the property of exponents that states $a^m \cdot a^n = a^{m+n}$, we can combine $s^{-1}$ and $s$: $$ s^{-1} s = s^{-1+1} = s^{0} $$
- Simplify Further
Since $s^{0} = 1$, the expression now becomes: $$ 1 \cdot t = t $$
The simplified expression is $t$.
More Information
In algebra, simplifying expressions is essential for solving problems more efficiently. Knowing that $t^{0} = 1$ and applying the rules for exponents helps simplify expressions properly.
Tips
- Forgetting that $a^{0} = 1$ can lead to incorrect conclusions.
- Misapplying the exponent rules may cause mistakes when combining like terms.
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