this what i meant..Short answer .Raise the quanity in parenthesisto the indicated exponents and simplify the resulting expression.Express with positive exponents.(50x^2y^-4/200x^-2y^4)^3
(50x^2y^-4/200x^-2y^4)^3
First you can simplify inside the parens:
x^2/x^-2 = x^4
y^-4/y^4 = y^-8 = 1/y^8
50/200 = 1/4
so, now you are left with
(x^4/4y^8)^3 = x^12/64y^24
(3x^ay^bz^c) (-y^fz^g)
To raise the quantity in parentheses to the indicated exponents, we need to apply the exponent to each term within the parentheses. Let's simplify the expression step-by-step:
Step 1: Start by simplifying the numerator and denominator separately.
Numerator: (50x^2y^-4)^3
To raise the quantity (50x^2y^-4) to the exponent 3, we need to multiply the exponents within the parentheses by 3.
50^3 = 125, x^2 * 3 = x^6, and y^-4 * 3 = y^-12.
Therefore, (50x^2y^-4)^3 simplifies to (125x^6y^-12).
Denominator: (200x^-2y^4)^3
Similarly, raise each term within the parentheses to the exponent 3:
200^3 = 8000000, x^-2 * 3 = x^-6, and y^4 * 3 = y^12.
Thus, (200x^-2y^4)^3 simplifies to (8000000x^-6y^12).
Step 2: Combine the numerator and denominator:
(125x^6y^-12) / (8000000x^-6y^12)
Since the denominator has negative exponents, we can rewrite them as positive exponents by moving them to the numerator:
(125x^6y^-12) * (x^6y^12/8000000)
Now, multiply the numerators together and the denominators together:
(125x^6y^-12) * (x^6y^12) / (8000000)
Simplify:
125x^6 * x^6 * y^-12 * y^12 / 8000000
Combine the like terms:
125x^(6+6) * y^(-12+12) / 8000000
125x^12 * y^0 / 8000000
Since any term raised to the power of 0 equals 1, y^0 simplifies to 1:
125x^12 * 1 / 8000000
Finally, simplify the expression:
125x^12 / 8000000
This is the simplified version of the given expression.