What is 5x^2y^-3 over 25x^6y^2 in simplest form
(5/25) x^2 x^-6 y^-3 y^-2
(5/25) x^-4 y^-5
1/( 5 x^4 y^5)
To simplify the expression (5x^2y^-3) / (25x^6y^2), we'll use the rules of exponents and perform the division.
Step 1: Simplify the numerator and denominator separately.
For the numerator: 5x^2y^-3
Since y^-3 is the same as 1/y^3, the numerator becomes 5x^2 / y^3.
For the denominator: 25x^6y^2
Step 2: Divide: (5x^2/y^3) / (25x^6y^2)
To divide fractions, multiply the numerator of the first fraction by the reciprocal of the second fraction.
Multiply the numerator (5x^2) by the reciprocal of the denominator (25x^6y^2).
Final Step: Simplify the expression by canceling out like terms, if possible.
5x^2 / y^3 * 1 / (25x^6y^2) = (5x^2)/(25x^6*y^3*y^2)
Now, simplify the expression using the power of a quotient rule:
5x^2 / (25x^6*y^3*y^2) = 1 / (5x^4*y^5)
Hence, the simplified form of (5x^2y^-3) / (25x^6y^2) is 1 / (5x^4y^5).