(5y)² Write your answer without parentheses.

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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

  1. 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).

  2. Calculate the exponent for the coefficient The coefficient is 5. When we square it, we calculate: $$ 5^2 = 25 $$

  3. Calculate the exponent for the variable Next, we square the variable $y$: $$ y^2 = y^2 $$

  4. Combine the results Now we combine the results from the previous steps: $$ (5y)^2 = 25y^2 $$

  5. 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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