014. Powers and Index Notation

Learning Intentions

To know the meaning of the terms: powers, index form, basic numeral, base number and index number
To understand what $a^{b}$ means when $a$ and $b$ are whole numbers
write a product in index form if there are repeated factors
evaluate numeric expressions involving powers using multiplication

Identify the terms in:

a) $3^{4}$
b) $5^{2}$

Write in expanded form:

a) $2^{5}$
b) $4^{3}$
c) $10^{2}$

Write in index form:

a) $3 \times 3 \times 3 \times 3$
b) $5 \times 5 \times 5$
c) $2 \times 2 \times 2 \times 2 \times 2$

Evaluate using multiplication:

a) $2^{4}$
b) $3^{3}$
c) $5^{2}$

Evaluate expressions involving powers:

a) $2^{3} \times 4$
b) $3^{2} + 6$
c) $10^{2} - 25$

Identify the terms:

a) $4^{3}$
b) $7^{2}$

Write in expanded form:

a) $3^{4}$
b) $6^{3}$
c) $9^{2}$

Write in index form:

a) $2 \times 2 \times 2$
b) $4 \times 4 \times 4 \times 4$
c) $7 \times 7$

Evaluate:

a) $2^{5}$
b) $4^{3}$
c) $6^{2}$

Evaluate expressions:

a) $3^{2} \times 5$
b) $2^{4} + 3$
c) $5^{2} - 10$

Identify base and index:
a) $2^{3}$
b) $5^{4}$
c) $9^{2}$
Write in expanded form:
a) $3^{3}$
b) $4^{2}$
c) $6^{4}$
Write in index form:
a) $5 \times 5 \times 5$
b) $2 \times 2 \times 2 \times 2$
c) $8 \times 8$
Evaluate powers:
a) $2^{3}$
b) $3^{4}$
c) $5^{2}$
Evaluate expressions:
a) $2^{3} + 4$
b) $3^{2} \times 6$
c) $10^{2} - 30$
Mixed practice:
a) $4^{2} + 5$
b) $2^{5} \times 2$
c) $6^{2} - 8$

A cube has side length $3$ . The volume is $3^{3}$ . Evaluate the volume.
A square has side length $5$ . The area is $5^{2}$ . Find the area.
Find the value of $2^{4} + 3^{2}$ .
A number is written as $4^{3}$ . Write this as repeated multiplication and evaluate.
Evaluate $2^{3} \times 5^{2}$ .