%5E2%2F3.jpeg "(27x^-3 Y^6)^2/3")
Simplifying the Expression: (27x^-3 y^6)^2/3
In this article, we will explore how to simplify the expression (27x^-3 y^6)^2/3. This expression involves exponent rules, and we will break it down step by step to arrive at the simplified form.
Step 1: Understand the Expression
The given expression is (27x^-3 y^6)^2/3. To simplify this expression, we need to follow the order of operations (PEMDAS) and apply the exponent rules.
Step 2: Apply the Power Rule
The power rule states that (a^m)^n = a^(mn). In our case, we have (27x^-3 y^6)^2/3. To apply the power rule, we need to raise each term inside the parentheses to the power of 2/3.
Step 3: Raise 27 to the Power of 2/3
27^(2/3) = (3^3)^(2/3) = 3^2 = 9
Step 4: Raise x^-3 to the Power of 2/3
x^(-3*(2/3)) = x^-2
Step 5: Raise y^6 to the Power of 2/3
y^(6*(2/3)) = y^4
Step 6: Combine the Terms
Now, we can combine the terms to get the simplified expression:
(27x^-3 y^6)^2/3 = 9x^-2 y^4
Step 7: Simplify Further
We can simplify the expression further by rewriting x^-2 as 1/x^2:
(27x^-3 y^6)^2/3 = 9/x^2 y^4
And that's the final simplified expression!
Conclusion
In this article, we successfully simplified the expression (27x^-3 y^6)^2/3 by applying the power rule and following the order of operations. The final simplified expression is 9/x^2 y^4.
