%5E-1.jpeg "(x^-5y/y^3)^-1")
(x^-5y/y^3)^-1: Understanding the Exponent Rule
In algebra, working with exponents can be a bit tricky, but understanding the rules and properties of exponents can make it easier to simplify and evaluate expressions. In this article, we will explore the expression (x^-5y/y^3)^-1 and see how to simplify it using the exponent rule.
The Exponent Rule
The exponent rule, also known as the power rule, is a fundamental property of exponents that states:
a^m × a^n = a^(m+n)
This rule can be extended to include negative exponents, fractional exponents, and even complex exponents. But for now, let's focus on the simple case.
Simplifying the Expression
Now, let's take a closer look at the expression (x^-5y/y^3)^-1. We can start by applying the exponent rule to the numerator and denominator separately.
(x^-5y)^-1 = x^5y^-1
(y^3)^-1 = y^-3
So, the expression (x^-5y/y^3)^-1 becomes:
(x^5y^-1)/(y^-3)
Simplifying Further
We can simplify the expression further by combining the powers of y.
(x^5y^-1)/(y^-3) = x^5y^(3-1) = x^5y^2
And there you have it! The simplified expression is:
(x^-5y/y^3)^-1 = x^5y^2
Conclusion
In this article, we have seen how to simplify the expression (x^-5y/y^3)^-1 using the exponent rule. By applying the rule and combining like terms, we were able to simplify the expression to x^5y^2. Remember, understanding the exponent rule is key to working with expressions involving powers and roots.
