Question

Which of the following is equal to $x$?

• A. $x^{\frac{12}{7}}-x^{\frac{5}{7}}$
• B. $\sqrt[12]{12(x^4{)}^{\frac{1}{3}}}$
• C. ${\left(\sqrt{x^3}\right)}^{\frac{2}{3}}$
• D. $x^{\frac{12}{7}}\times x^{\frac{7}{12}}$

Answer 1

The correct option is C ${\left(\sqrt{x^3}\right)}^{\frac{2}{3}}$

Simplify each option:
Option A, $x^{\frac{12}{7}}-x^{\frac{5}{7}}$ cannot be simplified further, hence it is not equal to x
Option B, $\sqrt[12]{12(x^4{)}^{\frac{1}{3}}}$ on simplifying is equal to, $x^{\frac{1}{9}}$
Option C, ${\left(\sqrt{x^3}\right)}^{\frac{2}{3}}$ on simplifying is equal to, x
Option D, $x^{\frac{12}{7}}\times x^{\frac{7}{12}}$ on simplifying is equal to, $x^{\frac{193}{84}}$