(3a^5/b^3)^4 ÷ (-9a^3/b^6)^2

Question

(3a^5/b^3)^4 ÷ (-9a^3/b^6)^2

Answer 1

(3a⁵b³⁾⁴/(-9a³b⁶)²

 

Let's look at the numerator: (3a⁵b³)⁴=3⁴(a⁵)⁴(b³)⁴ =

                                                     81 a⁵⁽⁴⁾b³⁽⁴⁾ = 81a²⁰b¹²

 

Look at the denominator:  (-9a³b⁶)² = (-9)²(a³)²(b⁶)^{2 =}

                                                      81 a⁶b¹²

 

(81a²⁰b¹²)/(81a⁶b¹²) =

We can cancel out the 81/81 and the b¹²/b¹² leaving a²⁰/a⁶ = (a²⁰)(a^-6)

                                                                                      = a^(20-6)

                                                                                      = a¹⁴