In all the mathematical operations the numbers have an exponent, even when the exponent is not shown, it is understood that its exponent is 1, the mathematical operations with exponents have different rules that are explained below.
When a base have this exponent and the base is different from cero the resulting value will always be 1, as shown in this examples. since this exponent does not modify the base.
When a number or a letter does not have an visible exponent, it is known that naturally its exponent is 1, since this exponent does not modify the base.
when we multiply two or more powers having the same base, we must add the powers of each base and raise the base to this resulting power.
When we habe a base raised into a power and this power is raised into another power we multiply them, as we see in this example.
$$(3^3)^6 = 3^(3*6)=3^18 $$
$$(y^7)^5 =y^(7*5)= y^35$$
$$(n^8)^2 = n^(8*2)=n^16 $$
the quotient rule explains that when a division is made with exponents, they must be subtracted, we must have also similar bases to aply this law.
$$5^7/8^2=0.625^(7-2)=0.625^5$$
$$(x^7y^8)/(x^2y^4)=x^(7-2)y^(8-4)=x^5y^4$$
$$(5n^7m^8p)/ (-2n^3m^4)=-2.5n^(7-3)m^(8-4)p=-2.5n^4m^4p $$
Mathematics is the language with which God has written the universe.
- Galileo Galilei (1564/1642)
I have hardly ever known a mathematician who was capable of reasoning.
- Plato (427—347 B.C.E.)
Mathematics is the queen of the sciences.
- Carl Friedrich Gauss (1777/1855)
There is geometry in the humming of the strings, there is music in the spacing of the spheres (planets).
- Pythagoras (569/500 B.C.E)
The laws of nature are but the mathematical thoughts of God.
- Euclid( c. 300 B.C.E)
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