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Simplifying the Expression: (3x^-2y)(6xy^-3)
This article will guide you through simplifying the expression (3x^-2y)(6xy^-3). We'll break down each step to ensure understanding.
Understanding the Basics
- Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, x^2 means x multiplied by itself twice (x*x).
- Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. For example, x^-2 is the same as 1/x^2.
- Multiplying with Exponents: When multiplying variables with exponents, we add the exponents together if the bases are the same. For example, x^2 * x^3 = x^(2+3) = x^5.
Simplifying the Expression
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Rewriting Negative Exponents:
- Rewrite x^-2 as 1/x^2 and y^-3 as 1/y^3.
- The expression now becomes: (3 * (1/x^2) * y) * (6 * x * (1/y^3)).
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Rearranging Terms:
- Rearrange the terms to group like terms together: (3 * 6) * (1/x^2 * x) * (y * 1/y^3).
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Simplifying Multiplication:
- Multiply the numerical coefficients: 3 * 6 = 18.
- Multiply the x terms: (1/x^2) * x = x^(-2+1) = x^-1.
- Multiply the y terms: y * (1/y^3) = y^(1-3) = y^-2.
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Final Result:
- The simplified expression is 18x^-1y^-2.
Expressing in Positive Exponents
Remember, negative exponents can be rewritten as their reciprocals. Therefore, the simplified expression can also be expressed as:
18 / (xy^2)
Conclusion
By understanding the rules of exponents and applying them step-by-step, we successfully simplified the expression (3x^-2y)(6xy^-3). Remember that negative exponents represent reciprocals and that multiplying variables with exponents requires adding the exponents when the bases are the same.