question 2\nsimplify $\\left(\\frac{x^{3}x^{0}}{xx^{5}}\\right)^{2}$\n$x^{6}$\n$\\frac{1}{x^{6}}$\n$\\frac{1}…

question 2\nsimplify $\\left(\\frac{x^{3}x^{0}}{xx^{5}}\\right)^{2}$\n$x^{6}$\n$\\frac{1}{x^{6}}$\n$\\frac{1}{x^{-6}}$\n$\\frac{x^{6}}{x^{-12}}$\nquestion 3\nsimplify $\\left(\\frac{x^{5}}{x^{-2}}\\right)^{2}$\n$\\frac{1}{x^{14}}$\n$x^{14}$\n$x^{6}$\n$\\frac{1}{x^{6}}$

question 2\nsimplify $\\left(\\frac{x^{3}x^{0}}{xx^{5}}\\right)^{2}$\n$x^{6}$\n$\\frac{1}{x^{6}}$\n$\\frac{1}{x^{-6}}$\n$\\frac{x^{6}}{x^{-12}}$\nquestion 3\nsimplify $\\left(\\frac{x^{5}}{x^{-2}}\\right)^{2}$\n$\\frac{1}{x^{14}}$\n$x^{14}$\n$x^{6}$\n$\\frac{1}{x^{6}}$

Answer

Question 2

Explanation:

Step 1: Simplify the numerator and denominator using exponent rules

  • For the numerator: (x^{3}\cdot x^{0}=x^{3 + 0}=x^{3}) (using (a^{m}\cdot a^{n}=a^{m + n}) and (a^{0}=1) for (a\neq0)).
  • For the denominator: (x\cdot x^{5}=x^{1+5}=x^{6}) (using (a^{m}\cdot a^{n}=a^{m + n})).
  • So the fraction becomes (\frac{x^{3}}{x^{6}}).
  • Using (a^{m}\div a^{n}=a^{m - n}), (\frac{x^{3}}{x^{6}}=x^{3-6}=x^{-3}).
  • Now we have ((x^{-3})^{2}).
  • Using ((a^{m})^{n}=a^{mn}), ((x^{-3})^{2}=x^{-6}=\frac{1}{x^{6}}).

Answer:

(\frac{1}{x^{6}}) (the second option)

Question 3

Explanation:

Step 1: Simplify the fraction inside the parentheses

  • Using (a^{m}\div a^{n}=a^{m - n}), (\frac{x^{5}}{x^{-2}}=x^{5-(-2)}=x^{5 + 2}=x^{7}).
  • Now we have ((x^{7})^{2}).
  • Using ((a^{m})^{n}=a^{mn}), ((x^{7})^{2}=x^{7\times2}=x^{14}).

Answer:

(x^{14}) (the second option)