Question

1. \\(\left(\dfrac{50x^6}{2x^3}\

ight)^2\\)

Explanation:

Step1: Simplify the fraction inside the parentheses

First, simplify \(\frac{50x^6}{2x^3}\). The coefficient \(50\div2 = 25\), and for the variable part, using the rule of exponents \(\frac{x^m}{x^n}=x^{m - n}\), we have \(x^{6-3}=x^3\). So \(\frac{50x^6}{2x^3}=25x^3\).

Step2: Square the result

Now, square \(25x^3\) using the rule \((ab)^n=a^n b^n\). So \((25x^3)^2 = 25^2\times(x^3)^2\). Calculate \(25^2 = 625\) and \((x^3)^2=x^{3\times2}=x^6\) (using the rule \((x^m)^n = x^{mn}\)). Then multiply them together: \(625\times x^6=625x^6\).

Answer:

\(625x^6\)