Question

Fill in the blanks :

$\left[{\left(3^3\right)}^2\times 3^4\right]÷3^6=\_\_\_\_\_\_\_\_\_$

Answer 1

By the properties of exponent, we know that -

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

By using the above properties -

$$\begin{gathered} \left[{\left(3^3\right)}^2\times 3^4\right]÷3^6=\left[3^{3\times 2}\times 3^4\right]÷3^6 \\ =\left[3^6\times 3^4\right]÷3^6 \\ =3^{6+4}÷3^6 \\ =3^{10}÷3^6 \\ =3^{10-6} \\ =3^4=81 \end{gathered}$$

Hence, the correct answer is $81$.