Which expression is equivalent to 100w^5y^6 / 50w^7y^3 for all values of w and y where the expression is defined?
Understand the Problem
The question is asking for an equivalent expression to the given fraction involving the variables w and y, specifically for the expression 100w^5y^6 / 50w^7y^3. This involves simplifying the expression using the laws of exponents.
Answer
The equivalent expression is $\frac{2y^3}{w^2}$.
Answer for screen readers
The equivalent expression is $\frac{2y^3}{w^2}$.
Steps to Solve
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Simplify the numerical part
Start by simplifying the coefficients of the fraction:
$$ \frac{100}{50} = 2 $$
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Simplify the $w$ terms
Use the laws of exponents to simplify the $w$ terms:
$$ \frac{w^5}{w^7} = w^{5-7} = w^{-2} $$
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Simplify the $y$ terms
Now simplify the $y$ terms:
$$ \frac{y^6}{y^3} = y^{6-3} = y^{3} $$
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Combine the simplified components
Now combine all the simplifications:
$$ 2 w^{-2} y^{3} $$
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Write the final equivalent expression
The final expression can be expressed with positive exponents:
$$ \frac{2y^3}{w^2} $$
The equivalent expression is $\frac{2y^3}{w^2}$.
More Information
This expression shows how the original fraction can be simplified using the laws of exponents. It's important to remember that negative exponents indicate reciprocal values.
Tips
- Forgetting to simplify both the coefficients and the variables, which can lead to incorrect final results.
- Misapplying the laws of exponents, particularly when subtracting exponents.
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