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Simplifying Expressions: (x^2y^3)(x^-2y^-2)
In algebra, simplifying expressions is an essential skill to master. In this article, we will explore how to simplify the expression (x^2y^3)(x^-2y^-2).
Understanding Exponent Rules
Before we dive into simplifying the expression, let's review some essential exponent rules:
- Product of Powers:
a^m * a^n = a^(m+n) - Power of a Product:
(ab)^m = a^m * b^m - Quotient of Powers:
a^m / a^n = a^(m-n)
Simplifying the Expression
Now, let's apply these rules to simplify the expression (x^2y^3)(x^-2y^-2):
(x^2y^3)(x^-2y^-2) = x^(2+(-2)) * y^(3+(-2))
Using the product of powers rule, we can rewrite the expression as:
= x^(2-2) * y^(3-2)
= x^0 * y^1
= 1 * y
= y
Therefore, the simplified expression is y.
Conclusion
In this article, we have successfully simplified the expression (x^2y^3)(x^-2y^-2) using exponent rules. By applying the product of powers rule, we were able to simplify the expression to its simplest form, which is simply y.
