POWER REVISION

A power is a short way to express the multiplication of a number by itself several times.

9+9+9+9+9+9=9·6=54

9·9·9·9·9·9=96=531,441

HOW TO READ POWERS...

144

Fourteen to the power four

BASE

INDEX

SPECIAL CASES

72 73

SEVEN SQUARED SEVEN CUBED

a0=1 a1=a

CALCULATION WITH INDICES

Remember the order of the operations:

B rackets

I ndices

D ivisions

M ultiplications

A dditions

S ubtractions

6 + (4-2) · 22 = =6 + (2) · 22 = =6 + (2) · 4= =6 + 8 = =13

LAWS OF INDICES

• Multiplication of powers with the same base:

62 · 65= 6 · 6 · 6 · 6 · 6 · 6 · 6= 62+5=67

• Division of power with the same base:

35 · 33 = 3 · 3 · 3 · 3 · 3 · 3 · 3 · 3 = 35-3=32

• Power of a power:

(23)4= (2·2·2)4 = (2·2·2) · (2·2·2) · (2·2·2) · (2·2·2)= =23·4= 212

SQUARE ROOTS

Taking the square root is the opposite of squaring.

Sacar la raíz cuadrada es el contrario de elevar al cuadrado.

√121=11, because 112 = 121

The square root of 121 is 11 because 11 squared is 121.

La raíz cuadrada de 121 es 11 porque 11 al cuadrado es 121.

SQUARE NUMBERS

are numbers that result from squaring another number.

1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , 144...