Reading Material - English for Basic Mathematics
Unit 4
Powers and roots
Section 1 Powers
When we write 42 ( four squared ), or x2 ( x squared ), the 2 is called the power
or index.
a x a2 ( a times a squared ) is equal to a3 ( a cubed ).
a3 x a2 ( a cubed times a squared ) is equal to a5 ( a to the power of five, or a to
the fifth ( power )).
In this example we simply add the indices or powers.
( x2 )3 ( x squared all cubed ) is equal to x6 ( x to the power of six ).
This example shows that to raise a power to a power, we multiply the indices.
Practice 1
Read out the following :
1) a2 + b2 =
5) 4b2 x 2b2 =
9) 6a2 - 3a2 =
2) x2 + y2 =
6) 3y2 x y =
10) 6y2 : 3y2 =
3) p4
7) x5 : x2
y
=
n
8) z = ( x + y )2
4) x
Section 2 Roots
64 means the squared root of 64
3
27 means the cube root of 27
5
x
means the fifth root of x.
If we wish to find the root in, for example,
n
am
we must divide the index by the root
= a m n = a m / n
Practice 2
Read out following
1)
2)
4)
5)
7)
3
a6
8)
3)
3
5
a3
6)
a5
9)
10)
3
8a 6
16b 2
3
8 x6 y9
Section 3 Fractional and negative indices.
2
3
5
x is equal to
x 3 . Here the index (
2
) is fraction and is therefore called a
3
fractional index.
X2 : x4 = x –2 ( x to the ( power of ) minus 2 ), which is called a negative index.
Practice 3
Read out following and say what their value is :
1) 9
1
2
4) 16
1
2
1
2)
3)
8
3
25
5) 36
1
2
6) 64
7) 22
1
2
1
2
8)
5-1
9)
4-2
10) 2-3
Vocabulary practice
Fillin the blank spaces in the following sentences :
1) Any number to the ____________ of 0 ( nought ) is equal to ___________
2) To divide powers we ____________the _____________________________
3) To ____________ a ______________to a power, we______________the
indices.
4) a to the _____________of five divided ___________ a _________________
5) The _________________________________ of forty – nine is seven.
6)
7)
8)
9)
10) If ten liters oil weight eight kilograms, and a liter of water weighs one
kilogram, what is ratio of the relative density of oil and water ?
Powers and roots
Section 1 Powers
When we write 42 ( four squared ), or x2 ( x squared ), the 2 is called the power
or index.
a x a2 ( a times a squared ) is equal to a3 ( a cubed ).
a3 x a2 ( a cubed times a squared ) is equal to a5 ( a to the power of five, or a to
the fifth ( power )).
In this example we simply add the indices or powers.
( x2 )3 ( x squared all cubed ) is equal to x6 ( x to the power of six ).
This example shows that to raise a power to a power, we multiply the indices.
Practice 1
Read out the following :
1) a2 + b2 =
5) 4b2 x 2b2 =
9) 6a2 - 3a2 =
2) x2 + y2 =
6) 3y2 x y =
10) 6y2 : 3y2 =
3) p4
7) x5 : x2
y
=
n
8) z = ( x + y )2
4) x
Section 2 Roots
64 means the squared root of 64
3
27 means the cube root of 27
5
x
means the fifth root of x.
If we wish to find the root in, for example,
n
am
we must divide the index by the root
= a m n = a m / n
Practice 2
Read out following
1)
2)
4)
5)
7)
3
a6
8)
3)
3
5
a3
6)
a5
9)
10)
3
8a 6
16b 2
3
8 x6 y9
Section 3 Fractional and negative indices.
2
3
5
x is equal to
x 3 . Here the index (
2
) is fraction and is therefore called a
3
fractional index.
X2 : x4 = x –2 ( x to the ( power of ) minus 2 ), which is called a negative index.
Practice 3
Read out following and say what their value is :
1) 9
1
2
4) 16
1
2
1
2)
3)
8
3
25
5) 36
1
2
6) 64
7) 22
1
2
1
2
8)
5-1
9)
4-2
10) 2-3
Vocabulary practice
Fillin the blank spaces in the following sentences :
1) Any number to the ____________ of 0 ( nought ) is equal to ___________
2) To divide powers we ____________the _____________________________
3) To ____________ a ______________to a power, we______________the
indices.
4) a to the _____________of five divided ___________ a _________________
5) The _________________________________ of forty – nine is seven.
6)
7)
8)
9)
10) If ten liters oil weight eight kilograms, and a liter of water weighs one
kilogram, what is ratio of the relative density of oil and water ?