Question

Choose the correct word/answer and fill in the blanks :

$6^2\times 6^5÷6^3=\_\_\_\_\_\_\_\_(6^{10-3}/6^{7-3})$

Answer 1

By the properties of exponent, we know that -

$$\begin{gathered} a^x\times a^y=a^{x+y} \\ {a}^x÷a^y=a^{x-y} \end{gathered}$$

By using the above properties -

$$\begin{gathered} 6^2\times 6^5÷6^3=6^{2+5}÷6^3 \\ =6^7÷6^3 \\ =6^{7-3} \end{gathered}$$

Hence, the correct answer is $6^{7-3}$.