Write each of the following in index form

i) \(\dfrac{2}{3} \times \dfrac{2}{3} \times \dfrac{2}{3} \)

ii) \(\dfrac{3x}{5} \times \dfrac{3x}{5} \times \dfrac{3x}{5} \)

Write each of the following in index form

i) \( 2 \times a \times a \times b \times b \times b\)

ii) \(5xy \times 5xy \times 5xy\)

Express each of the following as the product of prime factors in index form

i) \(50\)

ii) \(400\)

Given that \(a=4,\,b=3\) and \(c=-2\) evaluate

i) \((ac)^2\)

ii) \(ab^2c\)

Evaluate \(\left( \dfrac{3}{4} \right)^2\) without using a calculator. 

Evaluate \((-6)^3\) without using a calculator. 

Write \(\dfrac{5}{7} \times \dfrac{5}{7} \times \dfrac{5}{7}\) in index notation. 

Write \(\dfrac{2x}{3} \times \dfrac{2x}{3} \times \dfrac{2x}{3}\) in index notation. 

Write \( 3 \times p \times q \times p \times q\) in index form. 

Write \( 3ab \times 3ba \times 3ab \) in index form. 

Express \(108\) as the product of its prime factors in index form. 

Express \(900\) as the product of its prime factors in index form. 

Given that \(p=2\) and \(q=-3\) evaluate

i) \(3p^2q\)

ii) \(\left(pq \right)^2\)