raise the quantity in parenthesis to the indicated exponent and simplify.
(-16x^-2y^3)^2
__________
80x^-2y^3
To raise the quantity (-16x^-2y^3) to the exponent of 2, you simply raise each term inside the parentheses to the exponent of 2.
Starting with (-16x^-2y^3)^2, we have:
((-16)^2 * (x^-2)^2 * (y^3)^2) / (80x^-2y^3)
First, let's simplify the terms within the parentheses:
((-16)^2 is 256
(x^-2)^2 is x^(-2 * 2) which simplifies to x^-4
(y^3)^2 is y^(3 * 2) which simplifies to y^6
Our expression becomes:
(256 * x^-4 * y^6) / (80x^-2y^3)
Next, let's simplify the terms with negative exponents:
x^-4 can be rewritten as 1/x^4
x^-2 can be rewritten as 1/x^2
Our expression becomes:
(256 * (1/x^4) * y^6) / (80 * (1/x^2) * y^3)
Now, let's simplify the expression further by canceling out common factors:
256/80 simplifies to 4/1 or simply 4
1/x^4 * 1/x^2 simplifies to 1/x^(4+2) which is 1/x^6
y^6/y^3 simplifies to y^(6-3) which is y^3
Our expression becomes:
(4 * y^3) / (x^6)
or simply 4y^3/x^6
Therefore, the simplified expression is 4y^3/x^6.