Fully simplify. (-5x²y⁵)²
Understand the Problem
The question is asking to simplify the expression (-5x²y⁵)². This involves applying the power of a product rule and exponent rules to combine and simplify the expression.
Answer
The simplified expression is \( 25x^4y^{10} \).
Answer for screen readers
The simplified expression is ( 25x^4y^{10} ).
Steps to Solve
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Apply the power of a product rule
Using the power of a product rule, we can express the square as:
$$ (-5x^2y^5)^2 = (-5)^2 (x^2)^2 (y^5)^2 $$ -
Calculate each component
Now, calculate each term separately:
$$ (-5)^2 = 25 $$
$$ (x^2)^2 = x^{2 \cdot 2} = x^4 $$
$$ (y^5)^2 = y^{5 \cdot 2} = y^{10} $$ -
Combine the results
Now we can combine the results of the calculations:
$$ 25x^4y^{10} $$
The simplified expression is ( 25x^4y^{10} ).
More Information
This simplification involved applying the power of a product rule, which states that when raising a product to a power, you can apply the exponent to each factor within the parentheses. The final result shows how each component contributes to the overall expression.
Tips
- Failing to square each part of the expression separately. Make sure to apply the exponent to every factor including the coefficient, ( x ), and ( y ).
- Incorrectly calculating the powers, especially when multiplying exponents. Remember to multiply the exponents when raising a power to a power.
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