%5E-1%2F2.jpeg "(m^2/m^1/3)^-1/2")
Simplifying Exponents: The Case of (m^2/m^1/3)^-1/2
When working with exponents, it's essential to understand how to simplify expressions that involve multiple exponents. In this article, we'll explore how to simplify the expression (m^2/m^1/3)^-1/2.
Breaking Down the Expression
Let's start by breaking down the given expression:
(m^2/m^1/3)^-1/2
This expression involves three main components:
- m^2: a base (m) raised to the power of 2
- m^1/3: a base (m) raised to the power of 1/3
- The entire expression raised to the power of -1/2
Simplifying the Expression
To simplify this expression, we'll follow the order of operations (PEMDAS) and work from the inside out.
Step 1: Simplify the Fractional Exponent
First, let's focus on the m^1/3 term. Since the exponent is a fraction, we can rewrite it as a radical:
m^1/3 = ∛m
Now, our expression becomes:
(m^2/∛m)^-1/2
Step 2: Simplify the Fraction
Next, let's simplify the fraction inside the parentheses:
m^2/∛m = m^(2-1/3)
To subtract the fractional exponent, we'll find a common denominator, which is 3:
m^(2-1/3) = m^(6/3 - 1/3) = m^(5/3)
So, our expression becomes:
(m^(5/3))^-1/2
Step 3: Simplify the Outer Exponent
Finally, we'll simplify the outer exponent:
(m^(5/3))^-1/2 = m^(-5/6)
And that's our final answer!
Conclusion
Simplifying exponents can be a complex process, but by following the order of operations and working step-by-step, we can break down even the most complicated expressions. In this case, we simplified (m^2/m^1/3)^-1/2 to m^(-5/6). Remember to take your time and follow the rules of exponentiation to ensure accuracy in your calculations.
