%5E2%2F10.jpeg "(2x^2yz^3)^2/10")
Simplifying the Expression: (2x^2yz^3)^2 / 10
This article will walk through the process of simplifying the expression (2x^2yz^3)^2 / 10. We'll break down each step and explain the rules used.
Understanding the Expression
The expression contains several elements:
- (2x^2yz^3)^2: This represents the square of a product of variables and constants.
- 10: This is a constant divisor.
Simplifying the Expression
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Expanding the Square: We begin by expanding the square: (2x^2yz^3)^2 = (2x^2yz^3) * (2x^2yz^3)
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Applying the Product of Powers Rule: We multiply the coefficients and add the exponents of the same variables: (2x^2yz^3) * (2x^2yz^3) = 2 * 2 * x^2 * x^2 * y * y * z^3 * z^3 = 4x^4y^2z^6
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Dividing by the Constant: Now, we divide the result by 10: (4x^4y^2z^6) / 10 = (2/5)x^4y^2z^6
Final Result
The simplified form of the expression (2x^2yz^3)^2 / 10 is (2/5)x^4y^2z^6.
Key Points to Remember
- Exponent Rules: When multiplying powers with the same base, add the exponents. When raising a power to another power, multiply the exponents.
- Coefficient Multiplication: Multiply the coefficients together.
- Constant Division: Divide the entire expression by the constant.