Question

${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$ can be represented as :

• A. ${14}^{\frac{4}{7}}$
• B. ${14}^{\frac{2}{7}}$
• C. ${14}^{\frac{4}{7}}$
• D. ${14}^{\frac{3}{7}}$

Answer 1

The correct option is B ${14}^{\frac{2}{7}}$

Given Expression: ${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$

For any positive real number '$a$' and integers '$m$' and '$n$', we define$a^m\times a^n=a^{m+n}$
So,
${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}={14}^{\frac{1}{7}+\frac{1}{7}}$
$={14}^{\frac{1+1}{7}}={14}^{\frac{2}{7}}$
Therefore, ${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$ can represented as ${14}^{\frac{2}{7}}$.