%5E-2%2F3-(a-1)%5E-1%2F3.jpeg "(a-1)^-2/3 (a-1)^-1/3")
Simplifying Expressions: (a-1)^-2/3 (a-1)^-1/3
In this article, we will explore the simplification of the expression (a-1)^-2/3 (a-1)^-1/3. This expression involves negative exponents and fractional exponents, which can be challenging to simplify. Let's break it down step by step.
Understanding Negative Exponents
Before we dive into the simplification, let's quickly review what negative exponents mean. A negative exponent indicates that the base is raised to a power that is the reciprocal of the exponent. For example, a^-n is equivalent to 1/a^n.
Simplifying the Expression
Now, let's simplify the expression (a-1)^-2/3 (a-1)^-1/3. We can start by rewriting the expression using the property of exponents that states a^m * a^n = a^(m+n).
(a-1)^-2/3 (a-1)^-1/3 = (a-1)^(-2/3 + -1/3)
Combine the exponents:
(a-1)^(-2/3 + -1/3) = (a-1)^(-1)
Simplify the expression:
(a-1)^(-1) = 1/(a-1)
And that's the simplified expression!
Conclusion
In this article, we have successfully simplified the expression (a-1)^-2/3 (a-1)^-1/3 to 1/(a-1). This was made possible by understanding the concept of negative exponents and applying the property of exponents. Simplifying expressions like this one can be challenging, but with practice and patience, you can become proficient in algebraic manipulations.
