%5E5%2F(6x%5E-1-y%5E-8)%5E2.jpeg "(2x^-3y^-2)^5/(6x^-1 Y^-8)^2")
Simplifying Exponents: (2x^-3y^-2)^5/(6x^-1 y^-8)^2
In this article, we will explore how to simplify the expression (2x^-3y^-2)^5/(6x^-1 y^-8)^2. This expression involves exponents with negative indices, which can be challenging to simplify. Let's break it down step by step.
Step 1: Simplify the numerator
The numerator is (2x^-3y^-2)^5. To simplify this expression, we need to apply the power rule of exponents, which states that (a^m)^n = a^(mn). In this case, m = -3 and n = 5, so we get:
(2x^-3y^-2)^5 = 2^5 * x^(-3*5) * y^(-2*5) = 32x^-15y^-10
Step 2: Simplify the denominator
The denominator is (6x^-1 y^-8)^2. Again, we apply the power rule of exponents:
(6x^-1 y^-8)^2 = 6^2 * x^(-1*2) * y^(-8*2) = 36x^-2y^-16
Step 3: Simplify the entire expression
Now that we have simplified both the numerator and denominator, we can simplify the entire expression:
(2x^-3y^-2)^5/(6x^-1 y^-8)^2 = 32x^-15y^-10 / 36x^-2y^-16
To simplify this expression, we can divide both the numerator and denominator by their greatest common factor, which is 4x^-2y^-10. This gives us:
32x^-15y^-10 / 36x^-2y^-16 = 8x^-13y^-6 / 9x^-2y^-6
Finally, we can cancel out the common terms x^-2 and y^-6:
8x^-13y^-6 / 9x^-2y^-6 = 8/9 * x^(-13+2) * y^(-6+6) = 8/9 * x^-11 * y^0
Since y^0 = 1, we can simplify the expression further:
(2x^-3y^-2)^5/(6x^-1 y^-8)^2 = 8/9 * x^-11
And that's the final answer!
