1Write in index form: (a) \( 3 \times 3 \times 3 \) (b) \( 5 \times 5 \times 5 \times 5 \) (c) \( a \times a \times a \times a \times a \)
2Write in index form: (a) \( 2 \times 2 \times 3 \times 3 \times 3 \times 3 \) (b) \( x \times x \times x \times y \times y \) (c) \( a \times a \times a \times a \times b \times b \times b \)
3Write in expanded form: (a) \( b^4 \) (b) \( C^3 \times C^2 \) (c) \( l^2 \)
4Write in expanded form: (a) \( a^2 \times b^2 \) (b) \( y^2 \times y^2 \times p \) (c) \( l^3 \times b^2 \times h^2 \)
5Write \( z \times z^3 \times z^2 \) in expanded form and then bring it back to index form.
6Write in index form: (a) \( 4x^2 \times x^2 \) (b) \( x^5 \times x^2 \) (c) \( 3x^3 \times 6x^3 \)
7A rectangle has length x units and breadth y units. (a) What is its area? (b) What is the area if both the length and the breadth are y units? (c) What is that area when y is 8?
8A solid has length, breadth and height of a, b and c units. (a) What is its volume? (b) What is the volume if all three measurements are a units? (c) What is the volume when a is 11 cm?
9Find the volume of a solid with length 8a, breadth 4a and height a units, and write the answer in index form.
10In \( 7^5 \), which part is the base and which is the index, and what does the whole term tell us?
11Work out \( 2^3 \) and \( 3^2 \) and compare them.
12Show the difference between \( 3x^2 \) and \( (3x)^2 \) by writing each in expanded form.
13A cube has every edge measuring 5 cm. Write its volume in index form and then find its value.