10x^3y^-2 over 15x^6y^-3 this equation is then the ^-3
First, separate the constant and the two variables and simplify.
10 / 15 = 2 / 3
x^3 / x^6 = 1 / x^3
y^-2 / y ^-3 (negative exponents - switch the numerator and denominator)
y^3 / y^2 = y^1 / 1
Now combine these three terms.
Numerator: 2 * 1 * y^1 = 2y
Denominator: 3 * x^3 * 1 = 3x^3
The entire fraction is to the power of -3. Because the exponent is negative, switch the numerator and denominator.
Now distribute the exponent of 3 to all terms.
Numerator: (3x^3)^3 = 27x^9
Denominator: (2y)^3 = 8y^3
Final answer: 27x^9 / 8y^3