(5y)² Write your answer without parentheses.
Understand the Problem
The question is asking us to simplify the expression (5y)² and write the answer without parentheses. To solve this, we will apply the exponent to both the coefficient and the variable.
Answer
$25y^2$
Answer for screen readers
The final answer is $25y^2$.
Steps to Solve
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Apply the exponent to the coefficient and variable We need to simplify the expression $(5y)^2$. This involves applying the exponent to both the coefficient (5) and the variable (y).
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Calculate the exponent for the coefficient The coefficient is 5. When we square it, we calculate: $$ 5^2 = 25 $$
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Calculate the exponent for the variable Next, we square the variable $y$: $$ y^2 = y^2 $$
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Combine the results Now we combine the results from the previous steps: $$ (5y)^2 = 25y^2 $$
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Write the final answer The final answer is: $$ 25y^2 $$
The final answer is $25y^2$.
More Information
This simplification follows the property of exponents that states $(ab)^n = a^n \cdot b^n$. Thus, squaring a product involves squaring each factor.
Tips
- Forgetting to square both parts: Some may only square the coefficient or only apply it to the variable. Remember to apply the exponent to both.
- Not simplifying the coefficient correctly: Make sure to perform the exponentiation carefully.
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