%5E2.jpeg "(-5xy^2)^2")
Simplifying (-5xy^2)^2
In mathematics, simplifying expressions often involves applying rules of exponents and order of operations. Let's break down how to simplify the expression (-5xy^2)^2.
Understanding the Exponent
The exponent "2" indicates that we are multiplying the base, which is (-5xy^2), by itself twice:
(-5xy^2)^2 = (-5xy^2) * (-5xy^2)
Applying the Rules
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Product of Powers: When multiplying powers with the same base, you add the exponents. In this case, we have x and y with exponents:
- x^1 * x^1 = x^(1+1) = x^2
- y^2 * y^2 = y^(2+2) = y^4
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Power of a Product: When raising a product to a power, you raise each factor to that power:
- (-5)^2 = 25
- (x^1)^2 = x^2
- (y^2)^2 = y^4
Simplifying the Expression
Combining these rules, we can simplify the entire expression:
(-5xy^2)^2 = (-5)^2 * x^2 * y^4 = 25x^2y^4
Conclusion
The simplified form of (-5xy^2)^2 is 25x^2y^4. By applying the rules of exponents and order of operations, we can effectively simplify expressions and arrive at their simplest forms.