(x^3y^6)^-2+(x^2y^4)^-3

Jasonbradley

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Jun 17, 2024

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Simplifying Expressions with Negative Exponents

This article will guide you through simplifying the expression (x^3y^6)^-2 + (x^2y^4)^-3. We will use the properties of exponents to break down the problem step by step.

Understanding Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. In simpler terms:

x^-n = 1/x^n

Applying the Properties of Exponents

1. Distributing the Exponent: We start by distributing the negative exponents to each term inside the parentheses:

   (x^3y^6)^-2 = x^(3*-2)y^(6*-2) = x^-6y^-12 (x^2y^4)^-3 = x^(2*-3)y^(4*-3) = x^-6y^-12

2. Converting Negative Exponents to Positive: Now, we apply the rule of negative exponents to make the exponents positive:

   x^-6y^-12 = 1/x^6y^12 x^-6y^-12 = 1/x^6y^12

3. Adding the Fractions: Since both terms have the same denominator (x^6y^12), we can directly add the numerators:

   1/x^6y^12 + 1/x^6y^12 = 2/x^6y^12

Final Answer

Therefore, the simplified expression of (x^3y^6)^-2 + (x^2y^4)^-3 is 2/x^6y^12.