Question

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

• A. (14)^{1/7 + 1/7}
• B. (14 x 14)^1/7
• C. (14²)^1/7
• D. All of the above

Answer 1

Answer: (A), (B), (C)

The correct options are
A

(14)^{1/7 + 1/7}

B

(14 x 14)^1/7

C

(14²)^1/7

For any positive real '$a$' 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,
${14}^{\frac{1}{7}+\frac{1}{7}}={14}^{\frac{2}{7}}=({14}^2{)}^{\frac{1}{7}}$