Name
Year 8 Algebra
Mini Quiz
Focus on index laws
Please show all of your working out and mathematical thinking and attempts for the relevant
questions
am  an = a m+n
a 0=1
(ab)
m
(law 1)
(law 3)
= a mb m
am  an = a m – n
(law 2)
( am )n = a m  n
(law 4)
(law 6)
(law 5)
Complete this table
INDEX FORM
FACTOR FORM
5
2
NUMERAL
 5 x 5 5  5
7
9
729
10 x 10
 10  10
1 000 00
Simplify, using the law of indices. For each question state which law(s) you have used
Refer to key facts box at the top of the test
SOLUTION
 a3
a)
a7
b)
(a 3 ) 7
c)
a7
d)
(5 b) 3
e)
b0
f)
(
g)
3(ab 2 ) 2
4(ab) 2
h)
(y 2) 2

a3
a 3
)
b
 (y 4) 3  y10
LAW (S) USED
m9 is a simplification of the expression m3 x m6.
Write down all the other expressions you can think of that simplify to m 9.
a, b and c are prime numbers.
a Write 8 × a × a × b × b × b × c × c × c × c as a product of prime factors in index form.
b If a = 2, b = 3 and c = 7, calculate the value of the basic numeral represented by
your answer above
Write the area of each of these shapes using index notation
Find the width of each of these shapes using index notation
Area = 24a3 m2
Area = 36x2 y4
Work out the area of this rectangle and simplify to the form
Nicole and Maddy have a big bag of 10-cent coins.
They decide to make 30 piles of coins, starting with one coin in the first pile, then 2
coins in the second pile, 4 coins in the third pile, 8 in the fourth pile and so on,
continuing to double the number of coins for each new pile.
Given that each 10 cent piece is 2mm thick find the heights of the
1st
5th
10th
15th
piles and the value dollar of each of these piles
20th
25th
and 30th
BONUS QUESTION solve these 2 problem using all of your index laws
5
(m4n ) 3
(mn) 6

( )
m2
n
5