Question

Simplify $\frac{{15}^2\times {12}^3}{{18}^2}$.

Answer 1

According to law of exponents $a^n\times a^m=a^{n+m}$ and $a^n÷a^m=a^{n-m}$

$$\begin{gathered} \frac{{15}^2\times {12}^3}{{18}^2}=\frac{{\left(5\times 3\right)}^2\times {\left(2^2\times 3\right)}^3}{{\left(3^2\times 2\right)}^2} \\ =\frac{5^2\times 3^2\times 2^6\times 3^3}{3^4\times 2^2} \\ =\frac{5^2\times 3^{2+3}\times 2^6}{3^4\times 2^2} \\ =5^2\times 3^{5-4}\times 2^{6-2} \\ =5^2\times 3^1\times 2^4 \\ =1200 \end{gathered}$$

Hence, the final answer is $1200$.