1. Simplify the following, leaving your answer in index form. (i) 4 5
__ 4 3
__ a
(ii) 2 6
__ 2 2
(ii) m4
___ m2
(iii) 10 6 (iii) n12
___ n4
___ 10
2. Simplify the following, leaving your answer in index form. (i) a7
3. x3
sweets were distributed equally among x2 sweets each child received.
4. n5 (iv) x8 (iv) n
__ n
__ x6
(v) b7
__ b2
(v) n3
__ n2
children. Find, in terms of x, how many
grams of sweets were distributed among n3 the mass of sweets that was given to each child.
5. One steel plate has a mass of x4 of x , the number of plates.
6. There are y4 children. Find, in terms of n, grams. If the mass of a number of steel plates is x10 y , how many soldiers are there in each row. 19.4 A power on a power Discuss and discover
Working with a classmate, copy and complete the table below. (Bracket)Power
(4)1
( 3 2 ( 5 2 (x3 (y4 (n4
)2 )3 )2 )3 )4
Expanded bracket 41
32 52 ×32 ×52 ×52 Written as a power
Written as a power of 4 = Written as a power of 3 = Written as a power of 5 = Written as a power of x = Written as a power of y = Written as a power of n =
4 1 3 4 5
By the end of this section you should be able to:
● simplify variables with powers in a bracket with a power outside the bracket
grams, fi nd, in terms rows with equal number of soldiers. If the total number of soldiers was y14 , fi nd, in terms of (vi) y8 (vi) x2
__ y3
__ x
Look carefully at the table to see if you can discover a rule (using powers). What have you learned about powers from completing this table?