Simplify y^5 / y^3.
Understand the Problem
The question is asking to simplify the fraction \( \frac{y^5}{y^3} \) and rewrite the expression in a simpler form.
Answer
$y^2$
Answer for screen readers
The simplified expression is $y^2$.
Steps to Solve
- Identify the expression to simplify
We have the expression $\frac{y^5}{y^3}$ and we want to simplify it.
- Apply the quotient rule of exponents
When dividing two powers with the same base, we subtract the exponents:
$$ \frac{y^a}{y^b} = y^{a-b} $$
For our problem:
$$ \frac{y^5}{y^3} = y^{5-3} $$
- Simplify the exponent
Now simplify the exponent:
$$ 5 - 3 = 2 $$
So we have:
$$ y^{5-3} = y^2 $$
The simplified expression is $y^2$.
More Information
This process illustrates how to simplify expressions involving exponents by using the laws of exponents. Understanding this rule helps in various algebraic simplifications.
Tips
- Not subtracting the exponents correctly: Ensure to perform the subtraction accurately and keep track of the base.
- Forgetting that $y$ is the same base: Sometimes students confuse different bases or forget to apply the exponent rules correctly.
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