Angol Matematika

Powers

•        Definition: a power of a number is the product obtained by multiplying the number by itself a given times. • •an=a•a•a•...a

•        ‘a' is called base and tells which number we have to multiply      

•        ‘n' is called exponent or index (indices) and tells how many times we have to multiply the base by itself

•        ‘aⁿ' is called power

•        When the base is 1, every power of it is 1.

•        0⁰ hasn’t got any meaning

•        When the base is 0, every power of it is 0.

•        When the index is a negative integer, we take the reciprocal of the number to the positive exponent (base cannot be 0)

•        When the index is 1, we get the number itself. •When the index is 0, we get 1.

•        When the index is two, the number has been 'squared'. •When the index is three, the number has been 'cubed'. •When the index is greater than three you say that it is multiplied 'to the power of'. 72 is 'seven squared',
3³ is 'three cubed',
3⁷ is 'three to the power of seven',
4⁵ is 'four to the power of five'.

Laws of same bases

•        when the bases are the same in a multiplication, you find the new power by just adding the exponents:

aⁿ•a^m =a^n+m

•        when the bases are the same in a division, you find the new power by just subtracting the exponents:aⁿ:a^m =a^n-m

Laws of same indices

•        when the indices are the same in a multiplication, you find the new power by just multiplying the bases:

aⁿ bⁿ =(ab)ⁿ

•        when the indices are the same in a division, you find the new power by just dividing the bases:

aⁿ:bⁿ =(a:b)ⁿ

Power of powers

•        when you have any power of a power: you multiply the exponents:

(aⁿ)^m=a^nm

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