Simplify. Express your answer using positive exponents. 5st^4 / 5s^3t^7
Understand the Problem
The question is asking to simplify the given algebraic fraction involving exponents and express the answer using only positive exponents.
Answer
The final answer is $$ \frac{1}{s^2 t^3} $$.
Answer for screen readers
The simplified expression is $$ \frac{1}{s^2 t^3} $$.
Steps to Solve
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Cancel out common factors in the numerator and denominator Since both the numerator and denominator have a common factor of 5, we can simplify this by canceling it out: $$ \frac{5st^4}{5s^3t^7} = \frac{st^4}{s^3t^7} $$
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Simplify the variables with exponents Now focus on simplifying the variables $s$ and $t$. For $s$, use the rule $a^m / a^n = a^{m-n}$: $$ \frac{s^1}{s^3} = s^{1-3} = s^{-2} $$ For $t$, apply the same rule: $$ \frac{t^4}{t^7} = t^{4-7} = t^{-3} $$
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Combine the results Now we can combine our results together: $$ \frac{st^4}{s^3t^7} = s^{-2}t^{-3} $$
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Express with positive exponents To express the answer with positive exponents, we can rewrite $s^{-2}$ and $t^{-3}$ as follows: $$ s^{-2} = \frac{1}{s^2}, \quad t^{-3} = \frac{1}{t^3} $$ Therefore, $$ s^{-2} t^{-3} = \frac{1}{s^2 t^3} $$
The simplified expression is $$ \frac{1}{s^2 t^3} $$.
More Information
The simplification process applies the laws of exponents, which help consolidate terms with the same base. This approach also emphasizes the importance of expressing results in a standardized form with positive exponents.
Tips
- Forgetting to cancel out common numerical factors first.
- Misapplying the exponent rules, leading to errors in simplifying the expressions.
- Not expressing the final answer using only positive exponents.
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