Alg1.2.4

From Exampleproblems

Simplify $\frac{(60^3)(128^2)}{(27^2)(48)}\,$

Writing the factors of the bases $\frac{((2^2)(3)(5))^3(2^7)^2}{(3^3)^2(2^2)(2^2)(3)}\,$

Now the result is,combining the indices with the same bases $\frac{(2^6)(3^3)(5^3)(2^{14})}{(3^6)(2^4)(3)}\,$

$\frac{(2)^{6+14}{3^3}(5^3)}{(3)^{6+1}(2^4)}\,$

Now evaluating the numerator and denominator $\frac{2^{20-4}(5^3)}{3^{7-3}}\,$

$\frac{2^{16}(5^3)}{3^4}\,$