User Manual

- 5 -
Prompts
Ask learners to think about whether brackets are needed as they input their calculations.
Ask learners to think how the columns for
2
x
and
( )
1
2
x
are related.
Ask learners to think how the columns for
3
x
and
( )
1
2
x
can be combined to give the column for
( )
3
2
x
.
Ask whether negative powers ever give negative numbers.
Extension questions
Ask learners to think about the laws of indices – they can deduce the definitions from the laws.
• Multiplying
n
a
by 1 does not change the number. So, writing 1 as a power of a must give the
power of a to be zero as it does not change the power when added.
• Multiply
n
a
by
n
a
−
. What happens to the answer? What happens to the powers?
• Raising
n
a
to the power
1
n
gives
1
a
. How does that imply that raising a number to the power
1
n
is the same as finding the n
th
root?
Ask learners to investigate whether you get the same answer if you square first and then cube root, and
when you do the same two operations in the opposite order. Which is easier?