Question

Simplify: $3^{-2}\times {81}^{\frac{3}{4}}÷{729}^{-\frac{1}{3}}$

(3 marks)

Answer 1

$3^{-2}\times {81}^{\frac{3}{4}}÷(729{)}^{-\frac{1}{3}}$

$\Rightarrow \frac{1}{9}\times (3^4{)}^{\frac{3}{4}}÷{\left[\right(9{)}^3]}^{-\frac{1}{3}}$

(1 mark)

$\Rightarrow \frac{1}{9}\times 27÷(9{)}^{-1}$

(1 mark)

$\Rightarrow \frac{1}{9}\times 27\times 9\Rightarrow 27$

(1 mark)