Question

What is the simplest form of the expression $(M^2{)}^{\frac{5}{6}}\times M^{\frac{1}{3}}$ ?

• A. $M^{\frac{2}{3}}$
• B. $M^{\frac{11}{6}}$
• C. $M^2$
• D. None of the above

Answer 1

The correct option is C $M^2$

$(M^2{)}^{\frac{5}{6}}\times M^{\frac{1}{3}}$
= $M^{2\times \frac{5}{6}}\times M^{\frac{1}{3}}$
[ Applying: $(a^m{)}^n$ = $a^{mn}$ ]
= $M^{\frac{5}{3}}\times M^{\frac{1}{3}}$
= $M^{\frac{5+1}{3}}$ = $M^2$

[ Applying: $a^m\times a^n$ = $a^{m+n}$]