Laws of Mathematics Index

Law of Exponets & Examples

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.

Exponent 0 Rule

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.

Examples $$2^0=1$$

$$x^0=1$$

One Exponent Rule

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.

Examples

$$3=3^1$$

$$7=7^1$$

$$9=9^1$$

Multiplication With Exponents

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.

Examples

$$a^3*a^6=a^9$$

$$x^(3/4)*x^(1/4)= x$$

$$y^4.5*y^12.9=y^17.4$$

Multiplying Exponents

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.

Examples

$$(3^3)^6 = 3^(3*6)=3^18$$

$$(y^7)^5 =y^(7*5)= y^35$$

$$(n^8)^2 = n^(8*2)=n^16$$

Dividing Exponents

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.

Examples

$$5^7/8^2=0.625^(7-2)=0.625^5$$

$$(x^7y^8)/(x^2y^4)=x^(7-2)y^(8-4)=x^5y^4$$

$$(5n^7m^8p)/ (-2n^3m^4)=-2.5n^(7-3)m^(8-4)p=-2.5n^4m^4p$$

Thoughts on Mathematics

Mathematics is the language with which God has written the universe.

I have hardly ever known a mathematician who was capable of reasoning.

Mathematics is the queen of the sciences.

There is geometry in the humming of the strings, there is music in the spacing of the spheres (planets).

The laws of nature are but the mathematical thoughts of God.

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