Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(6^2x^2y/y^3)^−2
To simplify the expression, let's break it down step by step:
First, let's work on the inside of the parentheses: (6^2x^2y/y^3)
To simplify the numerator, we raise 6^2 to the power of x^2 (using the property of exponents that states: (a^m)^n = a^(m*n)):
6^2x^2 = (6^2)^x^2 = 36^x^2
Now, let's simplify the denominator by raising y/y^3 to the power of -1 (using the property of exponents that states: (a/b)^n = a^n/b^n):
y/y^3 = (y/y^3)^-1 = (1/y^2)^-1 = 1/1^(-1)y^(-2) = y^2
Now that we have simplified the inside of the parentheses, we can rewrite the expression as:
(36^x^2y^2)^-2
To simplify further, we raise 36^x^2y^2 to the power of -2 (using the property of exponents that states: (a*b)^n = a^n * b^n):
(36^x^2y^2)^-2 = 36^(-2x^2) * y^(-2*2) = (1/36^(2x^2)) * y^(-4)
Thus, the simplified expression (6^2x^2y/y^3)^−2 is 1/36^(2x^2) * y^(-4).