Factors, Powers And Standard Form Worksheet Page 14
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21C
7
Work out the highest common factor of 2016 and 1512.
8
Tarik and Archie have the same amount of money.
Tarik’s money is all in 20p pieces and Archie’s money is all in 50p pieces.
What is the smallest amount of money that they could each have?
9
Amy is investigating the relationship between the LCM and the HCF.
a
Work out the HCF of 18 and 30.
Amy says that she can fi nd the LCM of 18 and 30 using the rule LCM 5 18 3 30
_______
b
.
HCF
Show working to check that Amy’s rule works.
2
AO
c
Show that Amy’s rule will also work for 16 and 40.
C
10
David has a pack of playing cards with some missing.
A normal pack of playing
cards contains 52 cards.
He arranges his playing cards into 15 rows of equal
length. He then rearranges his playing cards into 9 rows
of equal length.
3
AO
How many cards are missing from David’s pack?
10.6
Laws of indices and standard form
Keywords
Why learn this
Objectives
laws of indices,
You can use standard
C
B
Use laws of indices to multiply
standard form
form to write very
and divide numbers written in index notation
large and very small
Carry out calculations with numbers given in standard form
Carry out calculations with numbers given in standard form
B
numbers. The mass of
a water molecule is
Skills check
Skills check
about 3 3 10
kg.
226
1 Write each of these using index notation.
1 Write each of these using index notation.
a 2 3 2 3 2
a 2 3 2 3 2
b 7 3 7 3 7 3 7
b 7 3 7 3 7 3 7
c 8 3 8 3 8
d 3 3 3 3 3 3 3 3 3
2 Work out the value of
a 2
b 3
c 10
d 2
5
4
3
7
Laws of indices
To multiply powers of the same number you add the indices.
4
2
3 4
5
5 (4 3 4) 3 (4 3 4 3 4 3 4 3 4) 5 4
7
You can multiply in any order
so the brackets don’t matter.
Using the laws of indices:
4
2
3 4
5
5 4
2 1 5
5 4
7
To divide powers of the same number you subtract the indices.
5 6 3 6 3 6 3 6 3 6
5 6 3 6
_________________
You can cancel 6 three times at the
______
6
5
4 6
3
5 6
2
6 3 6 3 6
1
top and at the bottom of the fraction.
Using the laws of indices:
6
5
4 6
3
5 6
5 2 3
5 6
2
10.6 Laws of indices and standard form
171
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education