# Raising Rational Fraction to the Integer Power

In order to raise rational fraction P/Q to the natural n-power, we should raise to this power the numerator and denominator of fraction separately; the first expression is numerator and second expression is denominator of the result: color(blue)((P/Q)^n=P^n/Q^n) .

Example 1. Convert power into fraction: ((2x^2y^3)/(3z^5))^3.

((2x^2y^3)/(3z^5))^3=(2x^2y^3)^3/(3z^5)^3=(8x^6y^9)/(27z^15) . When we raise fraction to the integer negative power we use the identity (P/Q)^(-n)=(Q/P)^n, that is correct for all values of variables, for which P!=0 and Q!=0.

Example 2. Convert power into fraction: (((a+b)^2(a-b)^3)/(a+2b)^4)^(-5).

(((a+b)^2(a-b)^3)/(a+2b)^4)^(-5)=(((a+2b)^4)/((a+b)^2(a-b)^3))^5=(a+2b)^20/((a+b)^10(a-b)^15) .