Question

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

• A. ${14}^{\frac{1}{7}+\frac{1}{7}}$
• B. ($14\times 14{)}^{\frac{1}{7}}$
• C. (${14}^2{)}^{\frac{1}{7}}$
• D. All of the above

Answer 1

The correct option is D

All of the above

For any positive real number 'a' and integers 'm' and 'n' we define

$a^m\times a^n=a^{m+n}$ and ${\left(a^m\right)}^n=a^{mn}$

$\text{Here,}a=14,m=n=\frac{1}{7}$. So,

${14}^{\frac{1}{7}+\frac{1}{7}}={14}^{\frac{2}{7}}=({14}^2{)}^{\frac{1}{7}}$